What is the integral from 2 to-2 of (9r+8)^2 ?

The integral from 2 to-2 of (9r+8)^2 is -688

Popular >

integral from 2 to-2 of (9r+8)^2

\int_{2}^{- 2} (9 r + 8)^{2} d r

- 688

Solution steps

\int_{2}^{- 2} (9 r + 8)^{2} d r

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{- 2}^{2} (9 r + 8)^{2} d r

Expand

(9 r + 8)^{2} : 81 r^{2} + 144 r + 64

= - \int_{- 2}^{2} 81 r^{2} + 144 r + 64 d r

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}^{2} 81 r^{2} d r + \int_{- 2}^{2} 144 r d r + \int_{- 2}^{2} 64 d r)

\int_{- 2}^{2} 81 r^{2} d r = 432

\int_{- 2}^{2} 144 r d r = 0

\int_{- 2}^{2} 64 d r = 256

= - (432 + 0 + 256)

Simplify

= - 688

\int_{0}^{π} x cos (n) x d x

\int_{0}^{1} e^{5 x + 3} d x

\int_{0}^{2} (4 - x^{2})^{\frac{3}{2}} d x

\int_{0}^{5} 6 x \cdot f (x^{2} + 1) d x

\int_{x}^{x^{2}} sin (t^{2}) d t

What is the integral from 2 to-2 of (9r+8)^2 ?
The integral from 2 to-2 of (9r+8)^2 is -688