What is the integral from-1 to 5 of (x^{1/3}-x) ?

The integral from-1 to 5 of (x^{1/3}-x) is (15*5^{1/3}-3)/4-12

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from-1 to 5 of (x^{1/3}-x)

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

\frac{15 \cdot 5 ^{\frac{1}{3}} - 3}{4} - 12

Decimal

- 6.33759 \dots

Solution steps

\int_{- 1}^{5} 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}^{5} x^{\frac{1}{3}} d x - \int_{- 1}^{5} x d x

\int_{- 1}^{5} x^{\frac{1}{3}} d x = \frac{15 \cdot 5 ^{\frac{1}{3}} - 3}{4}

\int_{- 1}^{5} x d x = 12

= \frac{15 \cdot 5 ^{\frac{1}{3}} - 3}{4} - 12

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

\int_{1}^{e} ln (x^{3}) d x

\int_{- 4}^{4} - ∣ x ∣ + 4 d x

\int_{3}^{5} (2 x + 9) d x

\int_{8}^{11} 2 x + 3 d x

What is the integral from-1 to 5 of (x^{1/3}-x) ?
The integral from-1 to 5 of (x^{1/3}-x) is (15*5^{1/3}-3)/4-12