integration of 5x^2 from defination
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Calculus Examples
Popular Problems Calculus Find the Anti-Derivative 5x^2
5
x
2
Write
5
x
2
as a function.
f
(
x
)
=
5
x
2
The function
F
(
x
)
can be found by finding the indefinite integral of the derivative
f
(
x
)
.
F
(
x
)
=
∫
f
(
x
)
d
x
Set up the integral to solve.
F
(
x
)
=
∫
5
x
2
d
x
Since
5
is constant with respect to
x
, move
5
out of the integral.
5
∫
x
2
d
x
By the Power Rule, the integral of
x
2
with respect to
x
is
1
3
x
3
.
5
(
1
3
x
3
+
C
)
Simplify the answer.
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5
3
x
3
+
C
The answer is the antiderivative of the function
f
(
x
)
=
5
x
2
.
F
(
x
)
=
5
3
x
3
+
C
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