What is the integral from-1 to 1 of x^{4/3}+4x^{1/3} ?

The integral from-1 to 1 of x^{4/3}+4x^{1/3} is 6/7

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integral from-1 to 1 of x^{4/3}+4x^{1/3}

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

\frac{6}{7}

Decimal

0.85714 \dots

Solution steps

\int_{- 1}^{1} x^{\frac{4}{3}} + 4 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_{- 1}^{1} x^{\frac{4}{3}} d x + \int_{- 1}^{1} 4 x^{\frac{1}{3}} d x

\int_{- 1}^{1} x^{\frac{4}{3}} d x = \frac{6}{7}

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

= \frac{6}{7} + 0

Simplify

= \frac{6}{7}

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What is the integral from-1 to 1 of x^{4/3}+4x^{1/3} ?
The integral from-1 to 1 of x^{4/3}+4x^{1/3} is 6/7