What is the integral from 0 to 6 of pi(-x^2+6x) ?

The integral from 0 to 6 of pi(-x^2+6x) is 36pi

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integral from 0 to 6 of pi(-x^2+6x)

\int_{0}^{6} π (- x^{2} + 6 x) d x

36 π

Decimal

113.09733 \dots

Solution steps

\int_{0}^{6} π (- x^{2} + 6 x) d x

Take the constant out:

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

= π \cdot \int_{0}^{6} - x^{2} + 6 x 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_{0}^{6} x^{2} d x + \int_{0}^{6} 6 x d x)

\int_{0}^{6} x^{2} d x = 72

\int_{0}^{6} 6 x d x = 108

= π (- 72 + 108)

Simplify

= 36 π

What is the integral from 0 to 6 of pi(-x^2+6x) ?
The integral from 0 to 6 of pi(-x^2+6x) is 36pi