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AP Calculus AB Flashcards: Fundamental Theorem Of Calculus Definite Intervals

Study Fundamental Theorem Of Calculus Definite Intervals in AP Calculus AB with focused flashcards that help you recognize the idea, recall the key rule, and apply it in practice-style prompts.

← Back to flashcard decks

What this deck covers

This deck focuses on Fundamental Theorem Of Calculus Definite Intervals, giving you a quick way to review the definitions, rules, and examples that matter most for AP Calculus AB.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

AP Calculus AB Flashcards: Fundamental Theorem Of Calculus Definite Intervals

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0 reviewed

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QUESTION

What is an antiderivative of $f(x) = 3x^2$ ?

Tap or drag to reveal answer

ANSWER

$F(x) = x^3 + C$ . Power rule: increase exponent by 1, divide by new exponent.

Swipe Right = I Know It! 🎉

Swipe Left = Still Learning

All flashcards

Flashcard 1: What is an antiderivative of $f(x) = 3x^2$ ?

Answer: $F(x) = x^3 + C$ . Power rule: increase exponent by 1, divide by new exponent.

Flashcard 2: Calculate $\int_1^3 (2x^2 - x)\,dx$ using the Fundamental Theorem.

Answer: $\frac{26}{3}$ . Use antiderivative $\frac{2x^3}{3} - \frac{x^2}{2}$ , evaluate at bounds.

Flashcard 3: Evaluate $\int_{-2}^2 (x^3 + 2x)\,dx$ using symmetry properties.

Answer: $0$ . Both functions are odd, so integral over symmetric interval is zero.

Flashcard 4: Evaluate $\int_0^4 (3x^2 + 2)\,dx$ using the Fundamental Theorem.

Answer:

Use antiderivative $x^3 + 2x$ , evaluate at bounds $4$ and $0$ .

Flashcard 5: State the Fundamental Theorem of Calculus, Part 1.

Answer: If $F$ is an antiderivative of $f$ on $[a,b]$ , then $\int_a^b f(x)\,dx = F(b) - F(a)$ . This allows calculation of definite integrals using antiderivatives.

Flashcard 6: Determine $\int_1^4 \frac{1}{x}\,dx$ .

Answer: $\ln(4)$ . Antiderivative of $\frac{1}{x}$ is $\ln(x)$ .

Flashcard 7: For $F(x) = \int_0^x e^t\,dt$ , find $F'(x)$ .

Answer: $e^x$ . By Part 2 of FTC, the derivative equals the integrand.

Flashcard 8: For $F(x) = \int_0^x \,\sin(t)\,dt$ , find $F'(x)$ .

Answer: $\sin(x)$ . By Part 2 of FTC, derivative equals the integrand.

Flashcard 9: What does the second part of the Fundamental Theorem allow us to compute?

Answer: The derivative of an integral function. It gives the rate of change of the area function.

Flashcard 10: Determine $\int_0^2 x^2\,dx$ using an antiderivative.

Answer: $\frac{8}{3}$ . Use antiderivative $\frac{x^3}{3}$ , evaluate at bounds.

Flashcard 11: Calculate $\int_1^3 (2x^2 - x)\,dx$ using the Fundamental Theorem.

Answer: $\frac{26}{3}$ . Use antiderivative $\frac{2x^3}{3} - \frac{x^2}{2}$ , evaluate at bounds.

Flashcard 12: What is the integral of $f(x) = e^x$ over $[0, 1]$ ?

Answer: $e - 1$ . Antiderivative of $e^x$ is $e^x$ ; evaluate at bounds.

Flashcard 13: What is a definite integral's geometric interpretation?

Answer: Net area between the curve and the x-axis over $[a, b]$ . Represents the signed area between curve and x-axis.

Flashcard 14: Find the derivative of $F(x) = \int_2^x \ln(t)\,dt$ .

Answer: $\ln(x)$ . By Part 2 of FTC, the derivative equals the integrand.

Flashcard 15: Find $\int_0^2 (4x^3 + x)\,dx$ using an antiderivative.

Answer:

Use antiderivative $x^4 + \frac{x^2}{2}$ , evaluate at bounds.

Flashcard 16: State the Fundamental Theorem of Calculus, Part 2.

Answer: If $f$ is continuous on $[a,b]$ , then $F(x) = \int_a^x f(t)\,dt$ is differentiable and $F'(x) = f(x)$ . Shows that differentiation and integration are inverse operations.

Flashcard 17: What is the definite integral of a constant $c$ over an interval $[a, b]$ ?

Answer: $c(b-a)$ . A constant function integrates to constant times interval length.

Flashcard 18: Compute $\int_{-1}^1 x^3\,dx$ using symmetry properties.

Answer:

Odd function over symmetric interval gives zero area.

Flashcard 19: Evaluate $\int_0^1 2x\,dx$ using the Fundamental Theorem of Calculus.

Answer:

Find antiderivative $x^2$ , then evaluate $1^2 - 0^2 = 1$ .

Flashcard 20: Determine $\int_1^3 x^2\,dx$ using an antiderivative.

Answer: $26/3$ . Use antiderivative $\frac{x^3}{3}$ , then evaluate at bounds.

Flashcard 21: What does the Fundamental Theorem of Calculus connect?

Answer: It connects differentiation and integration. They are inverse operations of each other.

Flashcard 22: Evaluate $\int_0^3 (x^2 + x + 1)\,dx$ using the Fundamental Theorem.

Answer:

Use antiderivative $\frac{x^3}{3} + \frac{x^2}{2} + x$ , evaluate at bounds.

Flashcard 23: Find $\int_0^4 (x^2 - 2)\,dx$ using the Fundamental Theorem.

Answer: $\frac{32}{3}$ . Use antiderivative $\frac{x^3}{3} - 2x$ , evaluate at bounds.

Flashcard 24: Determine $\int_0^1 (5x^2 - 3x)\,dx$ using an antiderivative.

Answer: $\frac{1}{3}$ . Use antiderivative $\frac{5x^3}{3} - \frac{3x^2}{2}$ , evaluate at bounds.

Flashcard 25: Evaluate $\int_0^1 (4x^3 - x)\,dx$ using the Fundamental Theorem.

Answer: $\frac{3}{4}$ . Use antiderivative $x^4 - \frac{x^2}{2}$ , evaluate at bounds.

Flashcard 26: What is the result of $\int_0^2 1\,dx$ ?

Answer:

Integral of constant $1$ over interval length $2$ .

Flashcard 27: Find $\int_0^1 (x^2 + 2x)\,dx$ using an antiderivative.

Answer: $\frac{7}{3}$ . Use antiderivative $\frac{x^3}{3} + x^2$ , evaluate at bounds.

Flashcard 28: What is the integral of $f(x) = \cos(x)$ over $[0, \pi]$ ?

Answer:

Antiderivative is $\sin(x)$ ; $\sin(\pi) - \sin(0) = 0$ .

Flashcard 29: What is the integral of $f(x) = 1/x$ over $[1, e]$ ?

Answer:

Antiderivative of $\frac{1}{x}$ is $\ln(x)$ ; $\ln(e) - \ln(1) = 1$ .

Flashcard 30: Calculate $\int_0^1 (x^3 + 1)\,dx$ using the Fundamental Theorem.

Answer: $\frac{5}{4}$ . Use antiderivative $\frac{x^4}{4} + x$ , evaluate at bounds.

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AP Calculus AB Flashcards: Fundamental Theorem Of Calculus Definite Intervals

Study Fundamental Theorem Of Calculus Definite Intervals in AP Calculus AB with focused flashcards that help you recognize the idea, recall the key rule, and apply it in practice-style prompts.

← Back to flashcard decks

What this deck covers

This deck focuses on Fundamental Theorem Of Calculus Definite Intervals, giving you a quick way to review the definitions, rules, and examples that matter most for AP Calculus AB.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

AP Calculus AB Flashcards: Fundamental Theorem Of Calculus Definite Intervals

/ 30

0 reviewed

0% Complete

0 reviewing

QUESTION

What is an antiderivative of $f(x) = 3x^2$ ?

Tap or drag to reveal answer

ANSWER

$F(x) = x^3 + C$ . Power rule: increase exponent by 1, divide by new exponent.

Swipe Right = I Know It! 🎉

Swipe Left = Still Learning

All flashcards

Flashcard 1: What is an antiderivative of $f(x) = 3x^2$ ?

Answer: $F(x) = x^3 + C$ . Power rule: increase exponent by 1, divide by new exponent.

Flashcard 2: Calculate $\int_1^3 (2x^2 - x)\,dx$ using the Fundamental Theorem.

Answer: $\frac{26}{3}$ . Use antiderivative $\frac{2x^3}{3} - \frac{x^2}{2}$ , evaluate at bounds.

Flashcard 3: Evaluate $\int_{-2}^2 (x^3 + 2x)\,dx$ using symmetry properties.

Answer: $0$ . Both functions are odd, so integral over symmetric interval is zero.

Flashcard 4: Evaluate $\int_0^4 (3x^2 + 2)\,dx$ using the Fundamental Theorem.

Answer:

Use antiderivative $x^3 + 2x$ , evaluate at bounds $4$ and $0$ .

Flashcard 5: State the Fundamental Theorem of Calculus, Part 1.

Answer: If $F$ is an antiderivative of $f$ on $[a,b]$ , then $\int_a^b f(x)\,dx = F(b) - F(a)$ . This allows calculation of definite integrals using antiderivatives.

Flashcard 6: Determine $\int_1^4 \frac{1}{x}\,dx$ .

Answer: $\ln(4)$ . Antiderivative of $\frac{1}{x}$ is $\ln(x)$ .

Flashcard 7: For $F(x) = \int_0^x e^t\,dt$ , find $F'(x)$ .

Answer: $e^x$ . By Part 2 of FTC, the derivative equals the integrand.

Flashcard 8: For $F(x) = \int_0^x \,\sin(t)\,dt$ , find $F'(x)$ .

Answer: $\sin(x)$ . By Part 2 of FTC, derivative equals the integrand.

Flashcard 9: What does the second part of the Fundamental Theorem allow us to compute?

Answer: The derivative of an integral function. It gives the rate of change of the area function.

Flashcard 10: Determine $\int_0^2 x^2\,dx$ using an antiderivative.

Answer: $\frac{8}{3}$ . Use antiderivative $\frac{x^3}{3}$ , evaluate at bounds.

Flashcard 11: Calculate $\int_1^3 (2x^2 - x)\,dx$ using the Fundamental Theorem.

Answer: $\frac{26}{3}$ . Use antiderivative $\frac{2x^3}{3} - \frac{x^2}{2}$ , evaluate at bounds.

Flashcard 12: What is the integral of $f(x) = e^x$ over $[0, 1]$ ?

Answer: $e - 1$ . Antiderivative of $e^x$ is $e^x$ ; evaluate at bounds.

Flashcard 13: What is a definite integral's geometric interpretation?

Answer: Net area between the curve and the x-axis over $[a, b]$ . Represents the signed area between curve and x-axis.

Flashcard 14: Find the derivative of $F(x) = \int_2^x \ln(t)\,dt$ .

Answer: $\ln(x)$ . By Part 2 of FTC, the derivative equals the integrand.

Flashcard 15: Find $\int_0^2 (4x^3 + x)\,dx$ using an antiderivative.

Answer:

Use antiderivative $x^4 + \frac{x^2}{2}$ , evaluate at bounds.

Flashcard 16: State the Fundamental Theorem of Calculus, Part 2.

Answer: If $f$ is continuous on $[a,b]$ , then $F(x) = \int_a^x f(t)\,dt$ is differentiable and $F'(x) = f(x)$ . Shows that differentiation and integration are inverse operations.

Flashcard 17: What is the definite integral of a constant $c$ over an interval $[a, b]$ ?

Answer: $c(b-a)$ . A constant function integrates to constant times interval length.

Flashcard 18: Compute $\int_{-1}^1 x^3\,dx$ using symmetry properties.

Answer:

Odd function over symmetric interval gives zero area.

Flashcard 19: Evaluate $\int_0^1 2x\,dx$ using the Fundamental Theorem of Calculus.

Answer:

Find antiderivative $x^2$ , then evaluate $1^2 - 0^2 = 1$ .

Flashcard 20: Determine $\int_1^3 x^2\,dx$ using an antiderivative.

Answer: $26/3$ . Use antiderivative $\frac{x^3}{3}$ , then evaluate at bounds.

Flashcard 21: What does the Fundamental Theorem of Calculus connect?

Answer: It connects differentiation and integration. They are inverse operations of each other.

Flashcard 22: Evaluate $\int_0^3 (x^2 + x + 1)\,dx$ using the Fundamental Theorem.

Answer:

Use antiderivative $\frac{x^3}{3} + \frac{x^2}{2} + x$ , evaluate at bounds.

Flashcard 23: Find $\int_0^4 (x^2 - 2)\,dx$ using the Fundamental Theorem.

Answer: $\frac{32}{3}$ . Use antiderivative $\frac{x^3}{3} - 2x$ , evaluate at bounds.

Flashcard 24: Determine $\int_0^1 (5x^2 - 3x)\,dx$ using an antiderivative.

Answer: $\frac{1}{3}$ . Use antiderivative $\frac{5x^3}{3} - \frac{3x^2}{2}$ , evaluate at bounds.

Flashcard 25: Evaluate $\int_0^1 (4x^3 - x)\,dx$ using the Fundamental Theorem.

Answer: $\frac{3}{4}$ . Use antiderivative $x^4 - \frac{x^2}{2}$ , evaluate at bounds.

Flashcard 26: What is the result of $\int_0^2 1\,dx$ ?

Answer:

Integral of constant $1$ over interval length $2$ .

Flashcard 27: Find $\int_0^1 (x^2 + 2x)\,dx$ using an antiderivative.

Answer: $\frac{7}{3}$ . Use antiderivative $\frac{x^3}{3} + x^2$ , evaluate at bounds.

Flashcard 28: What is the integral of $f(x) = \cos(x)$ over $[0, \pi]$ ?

Answer:

Antiderivative is $\sin(x)$ ; $\sin(\pi) - \sin(0) = 0$ .

Flashcard 29: What is the integral of $f(x) = 1/x$ over $[1, e]$ ?

Answer:

Antiderivative of $\frac{1}{x}$ is $\ln(x)$ ; $\ln(e) - \ln(1) = 1$ .

Flashcard 30: Calculate $\int_0^1 (x^3 + 1)\,dx$ using the Fundamental Theorem.

Answer: $\frac{5}{4}$ . Use antiderivative $\frac{x^4}{4} + x$ , evaluate at bounds.

Opening subject page...

AP Calculus AB Flashcards: Fundamental Theorem Of Calculus Definite Intervals

What this deck covers

How to use these flashcards

AP Calculus AB Flashcards: Fundamental Theorem Of Calculus Definite Intervals

All flashcards

Flashcard 1: What is an antiderivative of f(x)=3x2f(x) = 3x^2f(x)=3x2?

Flashcard 2: Calculate ∫13(2x2−x) dx\int_1^3 (2x^2 - x)\,dx∫13​(2x2−x)dx using the Fundamental Theorem.

Flashcard 3: Evaluate ∫−22(x3+2x) dx\int_{-2}^2 (x^3 + 2x)\,dx∫−22​(x3+2x)dx using symmetry properties.

Flashcard 4: Evaluate ∫04(3x2+2) dx\int_0^4 (3x^2 + 2)\,dx∫04​(3x2+2)dx using the Fundamental Theorem.

Flashcard 5: State the Fundamental Theorem of Calculus, Part 1.

Flashcard 6: Determine ∫141x dx\int_1^4 \frac{1}{x}\,dx∫14​x1​dx.

Flashcard 7: For F(x)=∫0xet dtF(x) = \int_0^x e^t\,dtF(x)=∫0x​etdt, find F′(x)F'(x)F′(x).

Flashcard 8: For F(x)=∫0x sin⁡(t) dtF(x) = \int_0^x \,\sin(t)\,dtF(x)=∫0x​sin(t)dt, find F′(x)F'(x)F′(x).

Flashcard 9: What does the second part of the Fundamental Theorem allow us to compute?

Flashcard 10: Determine ∫02x2 dx\int_0^2 x^2\,dx∫02​x2dx using an antiderivative.

Flashcard 11: Calculate ∫13(2x2−x) dx\int_1^3 (2x^2 - x)\,dx∫13​(2x2−x)dx using the Fundamental Theorem.

Flashcard 12: What is the integral of f(x)=exf(x) = e^xf(x)=ex over [0,1][0, 1][0,1]?

Flashcard 13: What is a definite integral's geometric interpretation?

Flashcard 14: Find the derivative of F(x)=∫2xln⁡(t) dtF(x) = \int_2^x \ln(t)\,dtF(x)=∫2x​ln(t)dt.

Flashcard 15: Find ∫02(4x3+x) dx\int_0^2 (4x^3 + x)\,dx∫02​(4x3+x)dx using an antiderivative.

Flashcard 16: State the Fundamental Theorem of Calculus, Part 2.

Flashcard 17: What is the definite integral of a constant ccc over an interval [a,b][a, b][a,b]?

Flashcard 18: Compute ∫−11x3 dx\int_{-1}^1 x^3\,dx∫−11​x3dx using symmetry properties.

Flashcard 19: Evaluate ∫012x dx\int_0^1 2x\,dx∫01​2xdx using the Fundamental Theorem of Calculus.

Flashcard 20: Determine ∫13x2 dx\int_1^3 x^2\,dx∫13​x2dx using an antiderivative.

Flashcard 21: What does the Fundamental Theorem of Calculus connect?

Flashcard 22: Evaluate ∫03(x2+x+1) dx\int_0^3 (x^2 + x + 1)\,dx∫03​(x2+x+1)dx using the Fundamental Theorem.

Flashcard 23: Find ∫04(x2−2) dx\int_0^4 (x^2 - 2)\,dx∫04​(x2−2)dx using the Fundamental Theorem.

Flashcard 24: Determine ∫01(5x2−3x) dx\int_0^1 (5x^2 - 3x)\,dx∫01​(5x2−3x)dx using an antiderivative.

Flashcard 25: Evaluate ∫01(4x3−x) dx\int_0^1 (4x^3 - x)\,dx∫01​(4x3−x)dx using the Fundamental Theorem.

Flashcard 26: What is the result of ∫021 dx\int_0^2 1\,dx∫02​1dx?

Flashcard 27: Find ∫01(x2+2x) dx\int_0^1 (x^2 + 2x)\,dx∫01​(x2+2x)dx using an antiderivative.

Flashcard 28: What is the integral of f(x)=cos⁡(x)f(x) = \cos(x)f(x)=cos(x) over [0,π][0, \pi][0,π]?

Flashcard 29: What is the integral of f(x)=1/xf(x) = 1/xf(x)=1/x over [1,e][1, e][1,e]?

Flashcard 30: Calculate ∫01(x3+1) dx\int_0^1 (x^3 + 1)\,dx∫01​(x3+1)dx using the Fundamental Theorem.

Opening subject page...

AP Calculus AB Flashcards: Fundamental Theorem Of Calculus Definite Intervals

What this deck covers

How to use these flashcards

AP Calculus AB Flashcards: Fundamental Theorem Of Calculus Definite Intervals

All flashcards

Flashcard 1: What is an antiderivative of f(x)=3x2f(x) = 3x^2f(x)=3x2?

Flashcard 2: Calculate ∫13(2x2−x) dx\int_1^3 (2x^2 - x)\,dx∫13​(2x2−x)dx using the Fundamental Theorem.

Flashcard 3: Evaluate ∫−22(x3+2x) dx\int_{-2}^2 (x^3 + 2x)\,dx∫−22​(x3+2x)dx using symmetry properties.

Flashcard 4: Evaluate ∫04(3x2+2) dx\int_0^4 (3x^2 + 2)\,dx∫04​(3x2+2)dx using the Fundamental Theorem.

Flashcard 5: State the Fundamental Theorem of Calculus, Part 1.

Flashcard 6: Determine ∫141x dx\int_1^4 \frac{1}{x}\,dx∫14​x1​dx.

Flashcard 7: For F(x)=∫0xet dtF(x) = \int_0^x e^t\,dtF(x)=∫0x​etdt, find F′(x)F'(x)F′(x).

Flashcard 8: For F(x)=∫0x sin⁡(t) dtF(x) = \int_0^x \,\sin(t)\,dtF(x)=∫0x​sin(t)dt, find F′(x)F'(x)F′(x).

Flashcard 9: What does the second part of the Fundamental Theorem allow us to compute?

Flashcard 10: Determine ∫02x2 dx\int_0^2 x^2\,dx∫02​x2dx using an antiderivative.

Flashcard 11: Calculate ∫13(2x2−x) dx\int_1^3 (2x^2 - x)\,dx∫13​(2x2−x)dx using the Fundamental Theorem.

Flashcard 12: What is the integral of f(x)=exf(x) = e^xf(x)=ex over [0,1][0, 1][0,1]?

Flashcard 13: What is a definite integral's geometric interpretation?

Flashcard 14: Find the derivative of F(x)=∫2xln⁡(t) dtF(x) = \int_2^x \ln(t)\,dtF(x)=∫2x​ln(t)dt.

Flashcard 15: Find ∫02(4x3+x) dx\int_0^2 (4x^3 + x)\,dx∫02​(4x3+x)dx using an antiderivative.

Flashcard 16: State the Fundamental Theorem of Calculus, Part 2.

Flashcard 17: What is the definite integral of a constant ccc over an interval [a,b][a, b][a,b]?

Flashcard 18: Compute ∫−11x3 dx\int_{-1}^1 x^3\,dx∫−11​x3dx using symmetry properties.

Flashcard 19: Evaluate ∫012x dx\int_0^1 2x\,dx∫01​2xdx using the Fundamental Theorem of Calculus.

Flashcard 20: Determine ∫13x2 dx\int_1^3 x^2\,dx∫13​x2dx using an antiderivative.

Flashcard 21: What does the Fundamental Theorem of Calculus connect?

Flashcard 22: Evaluate ∫03(x2+x+1) dx\int_0^3 (x^2 + x + 1)\,dx∫03​(x2+x+1)dx using the Fundamental Theorem.

Flashcard 23: Find ∫04(x2−2) dx\int_0^4 (x^2 - 2)\,dx∫04​(x2−2)dx using the Fundamental Theorem.

Flashcard 24: Determine ∫01(5x2−3x) dx\int_0^1 (5x^2 - 3x)\,dx∫01​(5x2−3x)dx using an antiderivative.

Flashcard 25: Evaluate ∫01(4x3−x) dx\int_0^1 (4x^3 - x)\,dx∫01​(4x3−x)dx using the Fundamental Theorem.

Flashcard 26: What is the result of ∫021 dx\int_0^2 1\,dx∫02​1dx?

Flashcard 27: Find ∫01(x2+2x) dx\int_0^1 (x^2 + 2x)\,dx∫01​(x2+2x)dx using an antiderivative.

Flashcard 28: What is the integral of f(x)=cos⁡(x)f(x) = \cos(x)f(x)=cos(x) over [0,π][0, \pi][0,π]?

Flashcard 29: What is the integral of f(x)=1/xf(x) = 1/xf(x)=1/x over [1,e][1, e][1,e]?

Flashcard 30: Calculate ∫01(x3+1) dx\int_0^1 (x^3 + 1)\,dx∫01​(x3+1)dx using the Fundamental Theorem.

Flashcard 1: What is an antiderivative of $f(x) = 3x^2$ ?

Flashcard 2: Calculate $\int_1^3 (2x^2 - x)\,dx$ using the Fundamental Theorem.

Flashcard 3: Evaluate $\int_{-2}^2 (x^3 + 2x)\,dx$ using symmetry properties.

Flashcard 4: Evaluate $\int_0^4 (3x^2 + 2)\,dx$ using the Fundamental Theorem.

Flashcard 6: Determine $\int_1^4 \frac{1}{x}\,dx$ .

Flashcard 7: For $F(x) = \int_0^x e^t\,dt$ , find $F'(x)$ .

Flashcard 8: For $F(x) = \int_0^x \,\sin(t)\,dt$ , find $F'(x)$ .

Flashcard 10: Determine $\int_0^2 x^2\,dx$ using an antiderivative.

Flashcard 11: Calculate $\int_1^3 (2x^2 - x)\,dx$ using the Fundamental Theorem.

Flashcard 12: What is the integral of $f(x) = e^x$ over $[0, 1]$ ?

Flashcard 14: Find the derivative of $F(x) = \int_2^x \ln(t)\,dt$ .

Flashcard 15: Find $\int_0^2 (4x^3 + x)\,dx$ using an antiderivative.

Flashcard 17: What is the definite integral of a constant $c$ over an interval $[a, b]$ ?

Flashcard 18: Compute $\int_{-1}^1 x^3\,dx$ using symmetry properties.

Flashcard 19: Evaluate $\int_0^1 2x\,dx$ using the Fundamental Theorem of Calculus.

Flashcard 20: Determine $\int_1^3 x^2\,dx$ using an antiderivative.

Flashcard 22: Evaluate $\int_0^3 (x^2 + x + 1)\,dx$ using the Fundamental Theorem.

Flashcard 23: Find $\int_0^4 (x^2 - 2)\,dx$ using the Fundamental Theorem.

Flashcard 24: Determine $\int_0^1 (5x^2 - 3x)\,dx$ using an antiderivative.

Flashcard 25: Evaluate $\int_0^1 (4x^3 - x)\,dx$ using the Fundamental Theorem.

Flashcard 26: What is the result of $\int_0^2 1\,dx$ ?

Flashcard 27: Find $\int_0^1 (x^2 + 2x)\,dx$ using an antiderivative.

Flashcard 28: What is the integral of $f(x) = \cos(x)$ over $[0, \pi]$ ?

Flashcard 29: What is the integral of $f(x) = 1/x$ over $[1, e]$ ?

Flashcard 30: Calculate $\int_0^1 (x^3 + 1)\,dx$ using the Fundamental Theorem.

Flashcard 1: What is an antiderivative of $f(x) = 3x^2$ ?

Flashcard 2: Calculate $\int_1^3 (2x^2 - x)\,dx$ using the Fundamental Theorem.

Flashcard 3: Evaluate $\int_{-2}^2 (x^3 + 2x)\,dx$ using symmetry properties.

Flashcard 4: Evaluate $\int_0^4 (3x^2 + 2)\,dx$ using the Fundamental Theorem.

Flashcard 6: Determine $\int_1^4 \frac{1}{x}\,dx$ .

Flashcard 7: For $F(x) = \int_0^x e^t\,dt$ , find $F'(x)$ .

Flashcard 8: For $F(x) = \int_0^x \,\sin(t)\,dt$ , find $F'(x)$ .

Flashcard 10: Determine $\int_0^2 x^2\,dx$ using an antiderivative.

Flashcard 11: Calculate $\int_1^3 (2x^2 - x)\,dx$ using the Fundamental Theorem.

Flashcard 12: What is the integral of $f(x) = e^x$ over $[0, 1]$ ?

Flashcard 14: Find the derivative of $F(x) = \int_2^x \ln(t)\,dt$ .

Flashcard 15: Find $\int_0^2 (4x^3 + x)\,dx$ using an antiderivative.

Flashcard 17: What is the definite integral of a constant $c$ over an interval $[a, b]$ ?

Flashcard 18: Compute $\int_{-1}^1 x^3\,dx$ using symmetry properties.

Flashcard 19: Evaluate $\int_0^1 2x\,dx$ using the Fundamental Theorem of Calculus.

Flashcard 20: Determine $\int_1^3 x^2\,dx$ using an antiderivative.

Flashcard 22: Evaluate $\int_0^3 (x^2 + x + 1)\,dx$ using the Fundamental Theorem.

Flashcard 23: Find $\int_0^4 (x^2 - 2)\,dx$ using the Fundamental Theorem.

Flashcard 24: Determine $\int_0^1 (5x^2 - 3x)\,dx$ using an antiderivative.

Flashcard 25: Evaluate $\int_0^1 (4x^3 - x)\,dx$ using the Fundamental Theorem.

Flashcard 26: What is the result of $\int_0^2 1\,dx$ ?

Flashcard 27: Find $\int_0^1 (x^2 + 2x)\,dx$ using an antiderivative.

Flashcard 28: What is the integral of $f(x) = \cos(x)$ over $[0, \pi]$ ?

Flashcard 29: What is the integral of $f(x) = 1/x$ over $[1, e]$ ?

Flashcard 30: Calculate $\int_0^1 (x^3 + 1)\,dx$ using the Fundamental Theorem.