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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

\frac{1}{4}

Decimal

0.25

Solution steps

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

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

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

= \frac{3}{4} - \frac{1}{2}

Simplify

\frac{3}{4} - \frac{1}{2} : \frac{1}{4}

= \frac{1}{4}

\int_{0}^{2} 15 x^{2} d x

\int_{- 8}^{3} - x^{2} - 3 x d x

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

\int_{0}^{1} x^{7} 1 + 3 x^{8} d x

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

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