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

The integral from-1 to 0 of x^{1/3}-x^{2/3} is -27/20

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

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

- \frac{27}{20}

Decimal

- 1.35

Solution steps

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

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

\int_{- 1}^{0} x^{\frac{2}{3}} d x = \frac{3 ( - 1 ) ^{\frac{2}{3}}}{5}

= \frac{3 ( - 1 ) ^{\frac{1}{3}}}{4} - \frac{3 ( - 1 ) ^{\frac{2}{3}}}{5}

Simplify

\frac{3 ( - 1 ) ^{\frac{1}{3}}}{4} - \frac{3 ( - 1 ) ^{\frac{2}{3}}}{5} : - \frac{27}{20}

= - \frac{27}{20}

\int \frac{2 x}{( x ^{2} + y ^{2} ) ^{2}} d x

\int x^{2} x^{3} + 13 d x

2 x^{2} + 10 x + 9

y = ln (7 x)

\frac{d}{d x} (cos (x) - 7 x)

What is the integral from-1 to 0 of x^{1/3}-x^{2/3} ?
The integral from-1 to 0 of x^{1/3}-x^{2/3} is -27/20