en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

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

Solution

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

Solution

\frac{32}{3}

+1

Decimal

10.66666 \dots

Solution steps

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

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

\int_{- 3}^{1} x^{2} d x = \frac{28}{3}

\int_{- 3}^{1} 2 x d x = - 8

= 12 - \frac{28}{3} - (- 8)

Simplify

12 - \frac{28}{3} - (- 8) : \frac{32}{3}

= \frac{32}{3}

Graph

Popular Examples

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

integral from 0 to 1 of 1/(xsqrt(1-x))

integral from 1 to 4 of (4x+sqrt(x))

integral from 1 to 5 of e^x

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

Frequently Asked Questions (FAQ)

What is the integral from-3 to 1 of 3-x^2-2x ?
The integral from-3 to 1 of 3-x^2-2x is 32/3