What is the integral from 0 to 6 of 2piy(36-y^2) ?

The integral from 0 to 6 of 2piy(36-y^2) is 648pi

Popular >

integral from 0 to 6 of 2piy(36-y^2)

\int_{0}^{6} 2 π y (36 - y^{2}) d y

648 π

Decimal Notation

2035.75203 \dots

Solution steps

\int_{0}^{6} 2 π y (36 - y^{2}) d y

Take the constant out:

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

= 2 π \cdot \int_{0}^{6} y (36 - y^{2}) d y

Expand

y (36 - y^{2}) : 36 y - y^{3}

= 2 π \cdot \int_{0}^{6} 36 y - y^{3} d y

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 2 π (\int_{0}^{6} 36 y d y - \int_{0}^{6} y^{3} d y)

\int_{0}^{6} 36 y d y = 648

\int_{0}^{6} y^{3} d y = 324

= 2 π (648 - 324)

Simplify

= 648 π

\int_{2}^{4} \frac{4}{x} d x

\int_{0}^{1} sech^{2} (5 x) d x

\int_{0}^{\infty} 25 e^{- 5 y} d y

\int_{0}^{l n (18)} tanh (x) d x

\int_{0}^{5} 2 (11 + 0.5 t) d t

What is the integral from 0 to 6 of 2piy(36-y^2) ?
The integral from 0 to 6 of 2piy(36-y^2) is 648pi