What is the integral from 1 to 5 of pi(sqrt(x-1))^2 ?

The integral from 1 to 5 of pi(sqrt(x-1))^2 is 8pi

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integral from 1 to 5 of pi(sqrt(x-1))^2

\int_{1}^{5} π (x - 1)^{2} d x

8 π

Decimal

25.13274 \dots

Solution steps

\int_{1}^{5} π (x - 1)^{2} d x

Take the constant out:

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

= π \cdot \int_{1}^{5} (x - 1)^{2} d x

Simplify

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

= π \cdot \int_{1}^{5} x - 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

= π (\int_{1}^{5} x d x - \int_{1}^{5} 1 d x)

\int_{1}^{5} x d x = 12

\int_{1}^{5} 1 d x = 4

= π (12 - 4)

Simplify

= 8 π

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What is the integral from 1 to 5 of pi(sqrt(x-1))^2 ?
The integral from 1 to 5 of pi(sqrt(x-1))^2 is 8pi