What is the integral from 1 to 4 of (x^2+2x+1) ?

The integral from 1 to 4 of (x^2+2x+1) is 39

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integral from 1 to 4 of (x^2+2x+1)

\int_{1}^{4} (x^{2} + 2 x + 1) d x

39

Solution steps

\int_{1}^{4} x^{2} + 2 x + 1 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}^{4} x^{2} d x + \int_{1}^{4} 2 x d x + \int_{1}^{4} 1 d x

\int_{1}^{4} x^{2} d x = 21

\int_{1}^{4} 2 x d x = 15

\int_{1}^{4} 1 d x = 3

= 21 + 15 + 3

Simplify

= 39

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What is the integral from 1 to 4 of (x^2+2x+1) ?
The integral from 1 to 4 of (x^2+2x+1) is 39