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 2 of (1-x^2)x

Solution

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

Solution

- \frac{9}{4}

+1

Decimal

- 2.25

Solution steps

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

Expand

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

= \int_{- 1}^{2} 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}^{2} x d x - \int_{- 1}^{2} x^{3} d x

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

\int_{- 1}^{2} x^{3} d x = \frac{15}{4}

= \frac{3}{2} - \frac{15}{4}

Simplify

\frac{3}{2} - \frac{15}{4} : - \frac{9}{4}

= - \frac{9}{4}

Graph

Popular Examples

integral from 0 to 1 of te^{(t^2)/2}

\int_{0}^{1} t e^{\frac{t ^{2}}{2}} d t

integral from 0 to 1 of 3x(1-x)^2

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

integral from 1/2 to 1 of 1

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

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

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

integral from 0 to 1 of (8x^3+3e^x+7)

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

Frequently Asked Questions (FAQ)

What is the integral from-1 to 2 of (1-x^2)x ?
The integral from-1 to 2 of (1-x^2)x is -9/4