Fundamental Theorem of Calculus: Definite Intervals
AP Calculus AB · Flashcards
AP CALCULUS AB · FLASHCARDS
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QUESTION
For
F
(
x
)
=
∫
0
x
sin
(
t
)
d
t
F(x) = \int_0^x \,\sin(t)\,dt
F
(
x
)
=
∫
0
x
sin
(
t
)
d
t
, find
F
′
(
x
)
F'(x)
F
′
(
x
)
.
QUESTION
Evaluate
∫
0
4
(
3
x
2
+
2
)
d
x
\int_0^4 (3x^2 + 2)\,dx
∫
0
4
(
3
x
2
+
2
)
d
x
using the Fundamental Theorem.
QUESTION
Determine
∫
1
4
1
x
d
x
\int_1^4 \frac{1}{x}\,dx
∫
1
4
x
1
d
x
.
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ANSWER
ln
(
4
)
\ln(4)
ln
(
4
)
. Antiderivative of
1
x
\frac{1}{x}
x
1
is
ln
(
x
)
\ln(x)
ln
(
x
)
.
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