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

The integral from 0 to 3 of pi(2sqrt(5y))^2 is pi90

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

\int_{0}^{3} π (2 5 y)^{2} d y

π 90

Decimal

282.74333 \dots

Solution steps

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

Apply Integration By Parts

: [20 y^{2} - \int 20 y d y]_{0}^{3}

= π [20 y^{2} - \int 20 y d y]_{0}^{3}

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

= π [20 y^{2} - 10 y^{2}]_{0}^{3}

Simplify

= π [10 y^{2}]_{0}^{3}

Compute the boundaries:

90

= π 90

y = F 4 x - x^{2}, (1, 3)

\int sin^{3} (1 - 2 x) cos^{3} (1 - 2 x) d x

\frac{d}{d x} (3 x - 4 x^{\frac{9}{10}})

\frac{d}{d x} (4 cos^{3} (x))

y = (9 x^{2} - 6 x + 2) (1 + 2 x), at x = 1

What is the integral from 0 to 3 of pi(2sqrt(5y))^2 ?
The integral from 0 to 3 of pi(2sqrt(5y))^2 is pi90