What is the integral from 0 to 1 of 6x^2-6x^3 ?

The integral from 0 to 1 of 6x^2-6x^3 is 1/2

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integral from 0 to 1 of 6x^2-6x^3

\int_{0}^{1} 6 x^{2} - 6 x^{3} d x

\frac{1}{2}

Solution steps

\int_{0}^{1} 6 x^{2} - 6 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}^{1} 6 x^{2} d x - \int_{0}^{1} 6 x^{3} d x

\int_{0}^{1} 6 x^{2} d x = 2

\int_{0}^{1} 6 x^{3} d x = \frac{3}{2}

= 2 - \frac{3}{2}

Simplify

2 - \frac{3}{2} : \frac{1}{2}

= \frac{1}{2}

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What is the integral from 0 to 1 of 6x^2-6x^3 ?
The integral from 0 to 1 of 6x^2-6x^3 is 1/2