What is the integral of pi(2sqrt(y))^2 ?

The integral of pi(2sqrt(y))^2 is 2piy^2+C

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integral of pi(2sqrt(y))^2

\int π (2 y)^{2} d y

2 π y^{2} + C

Solution steps

\int π (2 y)^{2} d y

Take the constant out:

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

= π \cdot \int (2 y)^{2} d y

Apply Integration By Parts

= π (4 y^{2} - \int 4 y d y)

\int 4 y d y = 2 y^{2}

= π (4 y^{2} - 2 y^{2})

Simplify

= 2 π y^{2}

Add a constant to the solution

= 2 π y^{2} + C

What is the integral of pi(2sqrt(y))^2 ?
The integral of pi(2sqrt(y))^2 is 2piy^2+C