What is the integral from 0 to 11 of 2piy(121-y^2) ?

The integral from 0 to 11 of 2piy(121-y^2) is (14641pi)/2

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integral from 0 to 11 of 2piy(121-y^2)

\int_{0}^{11} 2 π y (121 - y^{2}) d y

\frac{14641 π}{2}

Decimal Notation

22998.02902 \dots

Solution steps

\int_{0}^{11} 2 π y (121 - 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}^{11} y (121 - y^{2}) d y

Expand

y (121 - y^{2}) : 121 y - y^{3}

= 2 π \cdot \int_{0}^{11} 121 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}^{11} 121 y d y - \int_{0}^{11} y^{3} d y)

\int_{0}^{11} 121 y d y = \frac{14641}{2}

\int_{0}^{11} y^{3} d y = \frac{14641}{4}

= 2 π (\frac{14641}{2} - \frac{14641}{4})

Simplify

2 π (\frac{14641}{2} - \frac{14641}{4}) : \frac{14641 π}{2}

= \frac{14641 π}{2}

\frac{\partial}{\partial y} (x^{2} + y - e^{x + y})

\int \frac{x}{e ^{x}} d x

\int 2 x \cdot sec^{2} (3 x) d x

x \to 0 lim (e^{2 π})

\int e^{x} x d x

What is the integral from 0 to 11 of 2piy(121-y^2) ?
The integral from 0 to 11 of 2piy(121-y^2) is (14641pi)/2