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

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

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integral from 0 to 2 of pi(x^4-4x^2)

\int_{0}^{2} π (x^{4} - 4 x^{2}) d x

- π \frac{64}{15}

Decimal

- 13.40412 \dots

Solution steps

\int_{0}^{2} π (x^{4} - 4 x^{2}) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= π \cdot \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

= π (\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}

= π (\frac{32}{5} - \frac{32}{3})

Simplify

π (\frac{32}{5} - \frac{32}{3}) : - π \frac{64}{15}

= - π \frac{64}{15}

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