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

The integral from-2 to 2 of (2x+3)^2 is 172/3

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

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

\frac{172}{3}

Decimal

57.33333 \dots

Solution steps

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

Expand

(2 x + 3)^{2} : 4 x^{2} + 12 x + 9

= \int_{- 2}^{2} 4 x^{2} + 12 x + 9 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} 4 x^{2} d x + \int_{- 2}^{2} 12 x d x + \int_{- 2}^{2} 9 d x

\int_{- 2}^{2} 4 x^{2} d x = \frac{64}{3}

\int_{- 2}^{2} 12 x d x = 0

\int_{- 2}^{2} 9 d x = 36

= \frac{64}{3} + 0 + 36

Simplify

\frac{64}{3} + 0 + 36 : \frac{172}{3}

= \frac{172}{3}

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What is the integral from-2 to 2 of (2x+3)^2 ?
The integral from-2 to 2 of (2x+3)^2 is 172/3