What is the integral from 1 to 8 of x^2-4x-12 ?

The integral from 1 to 8 of x^2-4x-12 is -119/3

Popular >

integral from 1 to 8 of x^2-4x-12

\int_{1}^{8} x^{2} - 4 x - 12 d x

- \frac{119}{3}

Solution steps

\int_{1}^{8} x^{2} - 4 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_{1}^{8} x^{2} d x - \int_{1}^{8} 4 x d x - \int_{1}^{8} 12 d x

\int_{1}^{8} x^{2} d x = \frac{511}{3}

\int_{1}^{8} 4 x d x = 126

\int_{1}^{8} 12 d x = 84

= \frac{511}{3} - 126 - 84

Simplify

\frac{511}{3} - 126 - 84 : - \frac{119}{3}

= - \frac{119}{3}

\int_{2}^{4} x^{2} - 4 d x

\int_{0}^{5} (x^{2} - 4) d x

\int_{0}^{θ} \frac{2 x}{θ ^{2}} d x

\int_{0}^{π} 3 sec^{2} (x) d x

\int_{0}^{1} cos (x) + e^{2} d x

What is the integral from 1 to 8 of x^2-4x-12 ?
The integral from 1 to 8 of x^2-4x-12 is -119/3