What is the integral from 0 to 2 of (6x^2-3x^3) ?

The integral from 0 to 2 of (6x^2-3x^3) is 4

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integral from 0 to 2 of (6x^2-3x^3)

\int_{0}^{2} (6 x^{2} - 3 x^{3}) d x

4

Solution steps

\int_{0}^{2} 6 x^{2} - 3 x^{3} 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} 6 x^{2} d x - \int_{0}^{2} 3 x^{3} d x

\int_{0}^{2} 6 x^{2} d x = 16

\int_{0}^{2} 3 x^{3} d x = 12

= 16 - 12

Simplify

= 4

What is the integral from 0 to 2 of (6x^2-3x^3) ?
The integral from 0 to 2 of (6x^2-3x^3) is 4