en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from-1 to 3 of x(3-x^2)

Solution

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

Solution

- 8

Solution steps

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

Expand

x (3 - x^{2}) : 3 x - x^{3}

= \int_{- 1}^{3} 3 x - x^{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}^{3} 3 x d x - \int_{- 1}^{3} x^{3} d x

\int_{- 1}^{3} 3 x d x = 12

\int_{- 1}^{3} x^{3} d x = 20

= 12 - 20

Simplify

= - 8

Graph

Popular Examples

integral from 0 to 2pi of sin(x/2)

\int_{0}^{2 π} sin (\frac{x}{2}) d x

integral from-pi/4 to pi/4 of sec^2(x)

\int_{- \frac{π}{4}}^{\frac{π}{4}} sec^{2} (x) d x

integral from 1 to x^2 of (sin(t))/t

\int_{1}^{x^{2}} \frac{sin ( t )}{t} d t

integral from 1 to 4 of 3

\int_{1}^{4} 3 d x

integral from 1 to 2 of (x^2+1/(x^2))

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

Frequently Asked Questions (FAQ)

What is the integral from-1 to 3 of x(3-x^2) ?
The integral from-1 to 3 of x(3-x^2) is -8