What is the integral from 1 to-1 of (12r+11)^2 ?

The integral from 1 to-1 of (12r+11)^2 is -338

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integral from 1 to-1 of (12r+11)^2

\int_{1}^{- 1} (12 r + 11)^{2} d r

- 338

Solution steps

\int_{1}^{- 1} (12 r + 11)^{2} d r

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

= - \int_{- 1}^{1} (12 r + 11)^{2} d r

Expand

(12 r + 11)^{2} : 144 r^{2} + 264 r + 121

= - \int_{- 1}^{1} 144 r^{2} + 264 r + 121 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_{- 1}^{1} 144 r^{2} d r + \int_{- 1}^{1} 264 r d r + \int_{- 1}^{1} 121 d r)

\int_{- 1}^{1} 144 r^{2} d r = 96

\int_{- 1}^{1} 264 r d r = 0

\int_{- 1}^{1} 121 d r = 242

= - (96 + 0 + 242)

Simplify

= - 338

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What is the integral from 1 to-1 of (12r+11)^2 ?
The integral from 1 to-1 of (12r+11)^2 is -338