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

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

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

\int_{- 3}^{3} π (9 - x^{2}) d x

36 π

Decimal

113.09733 \dots

Solution steps

\int_{- 3}^{3} π (9 - x^{2}) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= π \cdot \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

= π (\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

= π (54 - 18)

Simplify

= 36 π

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