What is the integral from 0 to 1 of (x^{4/3}-2x^{1/3}) ?

The integral from 0 to 1 of (x^{4/3}-2x^{1/3}) is -15/14

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integral from 0 to 1 of (x^{4/3}-2x^{1/3})

\int_{0}^{1} (x^{\frac{4}{3}} - 2 x^{\frac{1}{3}}) d x

- \frac{15}{14}

Decimal

- 1.07142 \dots

Solution steps

\int_{0}^{1} x^{\frac{4}{3}} - 2 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} x^{\frac{4}{3}} d x - \int_{0}^{1} 2 x^{\frac{1}{3}} d x

\int_{0}^{1} x^{\frac{4}{3}} d x = \frac{3}{7}

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

= \frac{3}{7} - \frac{3}{2}

Simplify

\frac{3}{7} - \frac{3}{2} : - \frac{15}{14}

= - \frac{15}{14}

What is the integral from 0 to 1 of (x^{4/3}-2x^{1/3}) ?
The integral from 0 to 1 of (x^{4/3}-2x^{1/3}) is -15/14