en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from-3 to 2 of ((6-x)-(x^2))

Solution

\int_{- 3}^{2} ((6 - x) - (x^{2})) d x

Solution

\frac{125}{6}

+1

Solution steps

\int_{- 3}^{2} 6 - x - x^{2} 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}^{2} 6 d x - \int_{- 3}^{2} x d x - \int_{- 3}^{2} x^{2} d x

\int_{- 3}^{2} 6 d x = 30

\int_{- 3}^{2} x d x = - \frac{5}{2}

\int_{- 3}^{2} x^{2} d x = \frac{35}{3}

= 30 - (- \frac{5}{2}) - \frac{35}{3}

Simplify

30 - (- \frac{5}{2}) - \frac{35}{3} : \frac{125}{6}

= \frac{125}{6}

Popular Examples

(4x-3y)dx+(2y-3x)dy=0

(4 x - 3 y) d x + (2 y - 3 x) d y = 0

integral of (x+3)/(x^2+11x+18)

\int \frac{x + 3}{x ^{2} + 11 x + 18} d x

integral from 0 to 1 of sin(4pix)

\int_{0}^{1} sin (4 π x) d x

integral of (2x)/(3+x^2)

\int \frac{2 x}{3 + x ^{2}} d x

(dy)/(dt)=(yt-y)/((r^2+1))

\frac{d y}{d t} = \frac{y t - y}{( r ^{2} + 1 )}

Frequently Asked Questions (FAQ)

What is the integral from-3 to 2 of ((6-x)-(x^2)) ?
The integral from-3 to 2 of ((6-x)-(x^2)) is 125/6