What is the integral from 0 to 2 of x^4-4x^2 ?

The integral from 0 to 2 of x^4-4x^2 is -64/15

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integral from 0 to 2 of x^4-4x^2

\int_{0}^{2} x^{4} - 4 x^{2} d x

- \frac{64}{15}

Decimal

- 4.26666 \dots

Solution steps

\int_{0}^{2} x^{4} - 4 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^{4} d x - \int_{0}^{2} 4 x^{2} d x

\int_{0}^{2} x^{4} d x = \frac{32}{5}

\int_{0}^{2} 4 x^{2} d x = \frac{32}{3}

= \frac{32}{5} - \frac{32}{3}

Simplify

\frac{32}{5} - \frac{32}{3} : - \frac{64}{15}

= - \frac{64}{15}

What is the integral from 0 to 2 of x^4-4x^2 ?
The integral from 0 to 2 of x^4-4x^2 is -64/15