What is the integral from-1 to 1 of (3+2x)^2 ?

The integral from-1 to 1 of (3+2x)^2 is 62/3

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integral from-1 to 1 of (3+2x)^2

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

\frac{62}{3}

Decimal Notation

20.66666 \dots

Solution steps

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

Expand

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

= \int_{- 1}^{1} 9 + 12 x + 4 x^{2} 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_{- 1}^{1} 9 d x + \int_{- 1}^{1} 12 x d x + \int_{- 1}^{1} 4 x^{2} d x

\int_{- 1}^{1} 9 d x = 18

\int_{- 1}^{1} 12 x d x = 0

\int_{- 1}^{1} 4 x^{2} d x = \frac{8}{3}

= 18 + 0 + \frac{8}{3}

Simplify

18 + 0 + \frac{8}{3} : \frac{62}{3}

= \frac{62}{3}

\int_{0}^{2} \frac{x ^{3}}{3} d x

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\int_{1}^{2} (x^{2} - 1)^{2} d x

\int_{- 3}^{0} ln (y^{2} + 5) d y

What is the integral from-1 to 1 of (3+2x)^2 ?
The integral from-1 to 1 of (3+2x)^2 is 62/3