What is the integral from 2 to 11 of pi(sqrt(x-2))^2 ?

The integral from 2 to 11 of pi(sqrt(x-2))^2 is pi 81/2

Popular >

integral from 2 to 11 of pi(sqrt(x-2))^2

\int_{2}^{11} π (x - 2)^{2} d x

π \frac{81}{2}

Decimal

127.23450 \dots

Solution steps

\int_{2}^{11} 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}^{11} (x - 2)^{2} d x

Simplify

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

= π \cdot \int_{2}^{11} 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}^{11} x d x - \int_{2}^{11} 2 d x)

\int_{2}^{11} x d x = \frac{117}{2}

\int_{2}^{11} 2 d x = 18

= π (\frac{117}{2} - 18)

Join

\frac{117}{2} - 18 : \frac{81}{2}

= π \frac{81}{2}

\int_{0}^{1} - 4 x 5^{x} d x

\int_{2}^{4} (x^{2} - 6 x + 8) d x

\int_{- 1}^{0} \frac{1}{x ^{5}} d x

\int_{0}^{1} x cosh (x) d x

\int_{0}^{4 π} cos (x) d x

What is the integral from 2 to 11 of pi(sqrt(x-2))^2 ?
The integral from 2 to 11 of pi(sqrt(x-2))^2 is pi 81/2