What is the integral from-1 to 8 of (x^{1/3}-x) ?

The integral from-1 to 8 of (x^{1/3}-x) is -81/4

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integral from-1 to 8 of (x^{1/3}-x)

\int_{- 1}^{8} (x^{\frac{1}{3}} - x) d x

- \frac{81}{4}

Decimal

- 20.25

Solution steps

\int_{- 1}^{8} x^{\frac{1}{3}} - 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

= \int_{- 1}^{8} x^{\frac{1}{3}} d x - \int_{- 1}^{8} x d x

\int_{- 1}^{8} x^{\frac{1}{3}} d x = \frac{45}{4}

\int_{- 1}^{8} x d x = \frac{63}{2}

= \frac{45}{4} - \frac{63}{2}

Simplify

\frac{45}{4} - \frac{63}{2} : - \frac{81}{4}

= - \frac{81}{4}

\int_{1}^{2} \frac{x + 2}{3 - x} d x

\int_{0}^{1} x^{3} + 2 x^{2} - 3 x d x

\int_{- 2}^{2} 4 x^{3} d x

\int_{0}^{25} 85 - 3 25 - x d x

\int_{- 2}^{2} t^{3} d t

What is the integral from-1 to 8 of (x^{1/3}-x) ?
The integral from-1 to 8 of (x^{1/3}-x) is -81/4