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

The integral from 2 to 6 of pi(sqrt(x-2))^2 is 8pi

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

\int_{2}^{6} π (x - 2)^{2} d x

8 π

Decimal

25.13274 \dots

Solution steps

\int_{2}^{6} π (x - 2)^{2} d x

Take the constant out:

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

= π \cdot \int_{2}^{6} (x - 2)^{2} d x

Simplify

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

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

\int_{2}^{6} x d x = 16

\int_{2}^{6} 2 d x = 8

= π (16 - 8)

Simplify

= 8 π

What is the integral from 2 to 6 of pi(sqrt(x-2))^2 ?
The integral from 2 to 6 of pi(sqrt(x-2))^2 is 8pi