What is the integral from 0 to 3 of (sqrt(x^2+1))^2 ?

The integral from 0 to 3 of (sqrt(x^2+1))^2 is 12

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integral from 0 to 3 of (sqrt(x^2+1))^2

\int_{0}^{3} (x^{2} + 1)^{2} d x

12

Solution steps

\int_{0}^{3} (x^{2} + 1)^{2} d x

Simplify

(x^{2} + 1)^{2} : x^{2} + 1

= \int_{0}^{3} x^{2} + 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_{0}^{3} x^{2} d x + \int_{0}^{3} 1 d x

\int_{0}^{3} x^{2} d x = 9

\int_{0}^{3} 1 d x = 3

= 9 + 3

Simplify

= 12

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What is the integral from 0 to 3 of (sqrt(x^2+1))^2 ?
The integral from 0 to 3 of (sqrt(x^2+1))^2 is 12