What is the integral from 0 to 7 of pi(2sqrt(5y))^2 ?

The integral from 0 to 7 of pi(2sqrt(5y))^2 is pi490

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integral from 0 to 7 of pi(2sqrt(5y))^2

\int_{0}^{7} π (2 5 y)^{2} d y

π 490

Decimal

1539.38040 \dots

Solution steps

\int_{0}^{7} π (2 5 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}^{7} (2 5 y)^{2} d y

Apply Integration By Parts

= π [20 y^{2} - \int 20 y d y]_{0}^{7}

\int 20 y d y = 10 y^{2}

= π [20 y^{2} - 10 y^{2}]_{0}^{7}

Simplify

= π [10 y^{2}]_{0}^{7}

Compute the boundaries:

490

= π 490

What is the integral from 0 to 7 of pi(2sqrt(5y))^2 ?
The integral from 0 to 7 of pi(2sqrt(5y))^2 is pi490