What is the integral from 2 to 6 of (x+3)^2 ?

The integral from 2 to 6 of (x+3)^2 is 604/3

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integral from 2 to 6 of (x+3)^2

\int_{2}^{6} (x + 3)^{2} d x

\frac{604}{3}

Decimal

201.33333 \dots

Solution steps

\int_{2}^{6} (x + 3)^{2} d x

Expand

(x + 3)^{2} : x^{2} + 6 x + 9

= \int_{2}^{6} x^{2} + 6 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}^{6} x^{2} d x + \int_{2}^{6} 6 x d x + \int_{2}^{6} 9 d x

\int_{2}^{6} x^{2} d x = \frac{208}{3}

\int_{2}^{6} 6 x d x = 96

\int_{2}^{6} 9 d x = 36

= \frac{208}{3} + 96 + 36

Simplify

\frac{208}{3} + 96 + 36 : \frac{604}{3}

= \frac{604}{3}

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What is the integral from 2 to 6 of (x+3)^2 ?
The integral from 2 to 6 of (x+3)^2 is 604/3