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

The integral from 2 to-2 of (6x+5)^2 is -292

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

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

- 292

Solution steps

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

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

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

Expand

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

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

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

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

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

= - (192 + 0 + 100)

Simplify

= - 292

\int_{0}^{1} x \cdot 1 - x^{2} d x

\int_{2}^{5} (x^{3} + 3 x^{2} + 5 x + 9) d x

\int_{1}^{2} x (x^{2} + 1)^{3} d x

\int_{0}^{2 π} - 9 d t

\int_{1}^{\infty} t e^{- s t} d t

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