What is the integral from 2 to 6 of-x^2+8x-12 ?

The integral from 2 to 6 of-x^2+8x-12 is 32/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 2 to 6 of-x^2+8x-12

\int_{2}^{6} - x^{2} + 8 x - 12 d x

\frac{32}{3}

Decimal

10.66666 \dots

Solution steps

\int_{2}^{6} - x^{2} + 8 x - 12 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_{2}^{6} x^{2} d x + \int_{2}^{6} 8 x d x - \int_{2}^{6} 12 d x

\int_{2}^{6} x^{2} d x = \frac{208}{3}

\int_{2}^{6} 8 x d x = 128

\int_{2}^{6} 12 d x = 48

= - \frac{208}{3} + 128 - 48

Simplify

- \frac{208}{3} + 128 - 48 : \frac{32}{3}

= \frac{32}{3}

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

\int_{2}^{6} x (x^{2} + 7) d x

\int_{0}^{2} π x^{6} d x

\int_{0}^{y} \frac{1}{2} d x

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

What is the integral from 2 to 6 of-x^2+8x-12 ?
The integral from 2 to 6 of-x^2+8x-12 is 32/3