What is the integral from 3 to-3 of (6x+5)^2 ?

The integral from 3 to-3 of (6x+5)^2 is -798

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integral from 3 to-3 of (6x+5)^2

\int_{3}^{- 3} (6 x + 5)^{2} d x

- 798

Solution steps

\int_{3}^{- 3} (6 x + 5)^{2} d x

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

= - \int_{- 3}^{3} (6 x + 5)^{2} d x

Expand

(6 x + 5)^{2} : 36 x^{2} + 60 x + 25

= - \int_{- 3}^{3} 36 x^{2} + 60 x + 25 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}^{3} 36 x^{2} d x + \int_{- 3}^{3} 60 x d x + \int_{- 3}^{3} 25 d x)

\int_{- 3}^{3} 36 x^{2} d x = 648

\int_{- 3}^{3} 60 x d x = 0

\int_{- 3}^{3} 25 d x = 150

= - (648 + 0 + 150)

Simplify

= - 798

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What is the integral from 3 to-3 of (6x+5)^2 ?
The integral from 3 to-3 of (6x+5)^2 is -798