What is the integral from-3 to 3 of (sqrt(9-x^2))^2 ?

The integral from-3 to 3 of (sqrt(9-x^2))^2 is 36

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integral from-3 to 3 of (sqrt(9-x^2))^2

\int_{- 3}^{3} (9 - x^{2})^{2} d x

36

Solution steps

\int_{- 3}^{3} (9 - x^{2})^{2} d x

Simplify

(9 - x^{2})^{2} : 9 - x^{2}

= \int_{- 3}^{3} 9 - 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_{- 3}^{3} 9 d x - \int_{- 3}^{3} x^{2} d x

\int_{- 3}^{3} 9 d x = 54

\int_{- 3}^{3} x^{2} d x = 18

= 54 - 18

Simplify

= 36

What is the integral from-3 to 3 of (sqrt(9-x^2))^2 ?
The integral from-3 to 3 of (sqrt(9-x^2))^2 is 36