What is the integral from 0 to 9 of pi(2sqrt(3y))^2 ?

The integral from 0 to 9 of pi(2sqrt(3y))^2 is pi486

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integral from 0 to 9 of pi(2sqrt(3y))^2

\int_{0}^{9} π (2 3 y)^{2} d y

π 486

Decimal

1526.81402 \dots

Solution steps

\int_{0}^{9} π (2 3 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_{0}^{9} (2 3 y)^{2} d y

Apply Integration By Parts

= π [12 y^{2} - \int 12 y d y]_{0}^{9}

\int 12 y d y = 6 y^{2}

= π [12 y^{2} - 6 y^{2}]_{0}^{9}

Simplify

= π [6 y^{2}]_{0}^{9}

Compute the boundaries:

486

= π 486

What is the integral from 0 to 9 of pi(2sqrt(3y))^2 ?
The integral from 0 to 9 of pi(2sqrt(3y))^2 is pi486