What is the integral from 0 to 3 of pi(4sqrt(5y))^2 ?

The integral from 0 to 3 of pi(4sqrt(5y))^2 is pi360

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integral from 0 to 3 of pi(4sqrt(5y))^2

\int_{0}^{3} π (4 5 y)^{2} d y

π 360

Decimal

1130.97335 \dots

Solution steps

\int_{0}^{3} π (4 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}^{3} (4 5 y)^{2} d y

Apply Integration By Parts

: [80 y^{2} - \int 80 y d y]_{0}^{3}

= π [80 y^{2} - \int 80 y d y]_{0}^{3}

\int 80 y d y = 40 y^{2}

= π [80 y^{2} - 40 y^{2}]_{0}^{3}

Simplify

= π [40 y^{2}]_{0}^{3}

Compute the boundaries:

360

= π 360

\int_{- 1}^{6} (5 y - (y^{2} - 6)) d y

\int_{0}^{5} 22 + t d t

\int_{0}^{t} e^{t - x} d x

\int_{0}^{1} e^{x} 2 x d x

\int_{1}^{3} \frac{( x ^{3} - 1 )}{x ^{4}} d x

What is the integral from 0 to 3 of pi(4sqrt(5y))^2 ?
The integral from 0 to 3 of pi(4sqrt(5y))^2 is pi360