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Popular Calculus >

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

Solution

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

Solution

- 292

Solution steps

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

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

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

Expand

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

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

\int_{- 2}^{2} 36 r^{2} d r = 192

\int_{- 2}^{2} 60 r d r = 0

\int_{- 2}^{2} 25 d r = 100

= - (192 + 0 + 100)

Simplify

= - 292

Graph

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Frequently Asked Questions (FAQ)

What is the integral from 2 to-2 of (6r+5)^2 ?
The integral from 2 to-2 of (6r+5)^2 is -292