What is the integral from 0 to 1 of pi|x^4-x| ?

The integral from 0 to 1 of pi|x^4-x| is pi 3/10

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integral from 0 to 1 of pi|x^4-x|

\int_{0}^{1} π x^{4} - x d x

π \frac{3}{10}

Solution steps

\int_{0}^{1} π x^{4} - x d x

Eliminate Absolutes

= \int_{0}^{1} π (- x^{4} + x) d x

Take the constant out:

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

= π \cdot \int_{0}^{1} - x^{4} + x 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}^{1} x^{4} d x + \int_{0}^{1} x d x)

\int_{0}^{1} x^{4} d x = \frac{1}{5}

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

= π (- \frac{1}{5} + \frac{1}{2})

Join

- \frac{1}{5} + \frac{1}{2} : \frac{3}{10}

= π \frac{3}{10}

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What is the integral from 0 to 1 of pi|x^4-x| ?
The integral from 0 to 1 of pi|x^4-x| is pi 3/10