What is the integral from 0 to 2 of pi(8x-x^4) ?

The integral from 0 to 2 of pi(8x-x^4) is pi 48/5

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integral from 0 to 2 of pi(8x-x^4)

\int_{0}^{2} π (8 x - x^{4}) d x

π \frac{48}{5}

Decimal

30.15928 \dots

Solution steps

\int_{0}^{2} π (8 x - x^{4}) 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} 8 x - x^{4} 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} 8 x d x - \int_{0}^{2} x^{4} d x)

\int_{0}^{2} 8 x d x = 16

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

= π (16 - \frac{32}{5})

Join

16 - \frac{32}{5} : \frac{48}{5}

= π \frac{48}{5}

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What is the integral from 0 to 2 of pi(8x-x^4) ?
The integral from 0 to 2 of pi(8x-x^4) is pi 48/5