What is the integral from 0 to 1 of 5x^3-6x^{1/3} ?

The integral from 0 to 1 of 5x^3-6x^{1/3} is -13/4

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integral from 0 to 1 of 5x^3-6x^{1/3}

\int_{0}^{1} 5 x^{3} - 6 x^{\frac{1}{3}} d x

- \frac{13}{4}

Decimal

- 3.25

Solution steps

\int_{0}^{1} 5 x^{3} - 6 x^{\frac{1}{3}} 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_{0}^{1} 5 x^{3} d x - \int_{0}^{1} 6 x^{\frac{1}{3}} d x

\int_{0}^{1} 5 x^{3} d x = \frac{5}{4}

\int_{0}^{1} 6 x^{\frac{1}{3}} d x = \frac{9}{2}

= \frac{5}{4} - \frac{9}{2}

Simplify

\frac{5}{4} - \frac{9}{2} : - \frac{13}{4}

= - \frac{13}{4}

What is the integral from 0 to 1 of 5x^3-6x^{1/3} ?
The integral from 0 to 1 of 5x^3-6x^{1/3} is -13/4