What is the integral from 2 to 3 of (4+2x)^2 ?

The integral from 2 to 3 of (4+2x)^2 is 244/3

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integral from 2 to 3 of (4+2x)^2

\int_{2}^{3} (4 + 2 x)^{2} d x

\frac{244}{3}

Decimal

81.33333 \dots

Solution steps

\int_{2}^{3} (4 + 2 x)^{2} d x

Expand

(4 + 2 x)^{2} : 16 + 16 x + 4 x^{2}

= \int_{2}^{3} 16 + 16 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_{2}^{3} 16 d x + \int_{2}^{3} 16 x d x + \int_{2}^{3} 4 x^{2} d x

\int_{2}^{3} 16 d x = 16

\int_{2}^{3} 16 x d x = 40

\int_{2}^{3} 4 x^{2} d x = \frac{76}{3}

= 16 + 40 + \frac{76}{3}

Simplify

16 + 40 + \frac{76}{3} : \frac{244}{3}

= \frac{244}{3}

What is the integral from 2 to 3 of (4+2x)^2 ?
The integral from 2 to 3 of (4+2x)^2 is 244/3