What is the integral from 0 to 2 of (x^3+3x^2) ?

The integral from 0 to 2 of (x^3+3x^2) is 12

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integral from 0 to 2 of (x^3+3x^2)

\int_{0}^{2} (x^{3} + 3 x^{2}) d x

12

Solution steps

\int_{0}^{2} x^{3} + 3 x^{2} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{2} x^{3} d x + \int_{0}^{2} 3 x^{2} d x

\int_{0}^{2} x^{3} d x = 4

\int_{0}^{2} 3 x^{2} d x = 8

= 4 + 8

Simplify

= 12

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What is the integral from 0 to 2 of (x^3+3x^2) ?
The integral from 0 to 2 of (x^3+3x^2) is 12