What is the integral from-1 to 9 of x^{1/5}-x ?

The integral from-1 to 9 of x^{1/5}-x is -245/6+(15*9^{1/5})/2

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integral from-1 to 9 of x^{1/5}-x

\int_{- 1}^{9} x^{\frac{1}{5}} - x d x

- \frac{245}{6} + \frac{15 \cdot 9 ^{\frac{1}{5}}}{2}

Decimal

- 29.19449 \dots

Solution steps

\int_{- 1}^{9} x^{\frac{1}{5}} - 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}^{9} x^{\frac{1}{5}} d x - \int_{- 1}^{9} x d x

\int_{- 1}^{9} x^{\frac{1}{5}} d x = \frac{15 \cdot 9 ^{\frac{1}{5}}}{2} - \frac{5}{6}

\int_{- 1}^{9} x d x = 40

= \frac{15 \cdot 9 ^{\frac{1}{5}}}{2} - \frac{5}{6} - 40

Combine the fractions

- 40 - \frac{5}{6} : - \frac{245}{6}

= - \frac{245}{6} + \frac{15 \cdot 9 ^{\frac{1}{5}}}{2}

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What is the integral from-1 to 9 of x^{1/5}-x ?
The integral from-1 to 9 of x^{1/5}-x is -245/6+(15*9^{1/5})/2