What is the integral from-1 to 8 of x^{1/3}-x ?

The integral from-1 to 8 of x^{1/3}-x is -81/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from-1 to 8 of x^{1/3}-x

\int_{- 1}^{8} x^{\frac{1}{3}} - x d x

- \frac{81}{4}

Decimal

- 20.25

Solution steps

\int_{- 1}^{8} 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_{- 1}^{8} x^{\frac{1}{3}} d x - \int_{- 1}^{8} x d x

\int_{- 1}^{8} x^{\frac{1}{3}} d x = \frac{45}{4}

\int_{- 1}^{8} x d x = \frac{63}{2}

= \frac{45}{4} - \frac{63}{2}

Simplify

\frac{45}{4} - \frac{63}{2} : - \frac{81}{4}

= - \frac{81}{4}

\int_{0}^{x} \frac{1 - t}{t ^{2} + 15} d t

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

\int_{- 2}^{2} (2 x + 3)^{2} d x

\int_{0}^{π} (sin (x) + cos (y)) d x

\int_{2}^{3} (3 x + 1) d x

What is the integral from-1 to 8 of x^{1/3}-x ?
The integral from-1 to 8 of x^{1/3}-x is -81/4