What is the integral from 0 to 10 of 2piy(100-y^2) ?

The integral from 0 to 10 of 2piy(100-y^2) is 5000pi

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integral from 0 to 10 of 2piy(100-y^2)

\int_{0}^{10} 2 π y (100 - y^{2}) d y

5000 π

Decimal Notation

15707.96326 \dots

Solution steps

\int_{0}^{10} 2 π y (100 - 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}^{10} y (100 - y^{2}) d y

Expand

y (100 - y^{2}) : 100 y - y^{3}

= 2 π \cdot \int_{0}^{10} 100 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}^{10} 100 y d y - \int_{0}^{10} y^{3} d y)

\int_{0}^{10} 100 y d y = 5000

\int_{0}^{10} y^{3} d y = 2500

= 2 π (5000 - 2500)

Simplify

= 5000 π

\int x^{2} 0. 4^{- x} x d x

(4, 5), (1, - 3)

t^{2} y^{^{''}} - 11 t y^{^{'}} + 35 y = 0

\int \frac{x ^{4} + 8}{x ^{3}} d x

y^{^{''}} + y = 2 csc^{2} (t)

What is the integral from 0 to 10 of 2piy(100-y^2) ?
The integral from 0 to 10 of 2piy(100-y^2) is 5000pi