What is the integral from 0 to 2.5 of (x+2)^2 ?

The integral from 0 to 2.5 of (x+2)^2 is 27.70833…

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integral from 0 to 2.5 of (x+2)^2

\int_{0}^{2.5} (x + 2)^{2} d x

27.70833 \dots

Solution steps

\int_{0}^{2.5} (x + 2)^{2} d x

Expand

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

= \int_{0}^{2.5} x^{2} + 4 x + 4 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_{0}^{2.5} x^{2} d x + \int_{0}^{2.5} 4 x d x + \int_{0}^{2.5} 4 d x

\int_{0}^{2.5} x^{2} d x = 5.20833 \dots

\int_{0}^{2.5} 4 x d x = 12.5

\int_{0}^{2.5} 4 d x = 10

= 5.20833 \dots + 12.5 + 10

Simplify

= 27.70833 \dots

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What is the integral from 0 to 2.5 of (x+2)^2 ?
The integral from 0 to 2.5 of (x+2)^2 is 27.70833…