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

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

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 (x^2+x-6)

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

- \frac{125}{6}

Decimal Notation

- 20.83333 \dots

Solution steps

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

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

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

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

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

Simplify

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

= - \frac{125}{6}

\int_{0}^{x} e^{x} d x

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

\int_{0}^{x} cos (x) d x

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

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

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