Fundamental Theorem of Calculus: Definite Intervals
AP Calculus BC · Flashcards
AP CALCULUS BC · FLASHCARDS
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QUESTION
Find the integral of
f
(
x
)
=
4
x
3
−
x
2
+
2
f(x) = 4x^3 - x^2 + 2
f
(
x
)
=
4
x
3
−
x
2
+
2
from 0 to 1.
QUESTION
Calculate the integral of
f
(
x
)
=
1
x
2
f(x) = \frac{1}{x^2}
f
(
x
)
=
x
2
1
from 1 to 2.
QUESTION
Calculate the integral of
f
(
x
)
=
x
−
1
f(x) = x^{-1}
f
(
x
)
=
x
−
1
from 1 to 4.
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ANSWER
ln
(
4
)
\text{ln}(4)
ln
(
4
)
. Same as
∫
1
x
d
x
\int \frac{1}{x} dx
∫
x
1
d
x
, antiderivative is
ln
(
x
)
\ln(x)
ln
(
x
)
.
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