What is the integral from 0 to 1 of \sqrt[3]{x}-x ?

The integral from 0 to 1 of \sqrt[3]{x}-x is 1/4

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integral from 0 to 1 of \sqrt[3]{x}-x

\frac{1}{4}

Decimal

0.25

Solution steps

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} x d x = \frac{1}{2}

= \frac{3}{4} - \frac{1}{2}

Simplify

\frac{3}{4} - \frac{1}{2} : \frac{1}{4}

= \frac{1}{4}

What is the integral from 0 to 1 of \sqrt[3]{x}-x ?
The integral from 0 to 1 of \sqrt[3]{x}-x is 1/4