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

The integral from 0 to 3 of pi(4sqrt(3y))^2 is pi216

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

\int_{0}^{3} π (4 3 y)^{2} d y

π 216

Decimal

678.58401 \dots

Solution steps

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

Apply Integration By Parts

: [48 y^{2} - \int 48 y d y]_{0}^{3}

= π [48 y^{2} - \int 48 y d y]_{0}^{3}

\int 48 y d y = 24 y^{2}

= π [48 y^{2} - 24 y^{2}]_{0}^{3}

Simplify

= π [24 y^{2}]_{0}^{3}

Compute the boundaries:

216

= π 216

5^{4 x}

\frac{d}{d x} ((7 x^{4} + 10)^{5})

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\frac{d}{d y} (\frac{1}{x - y})

\int 35 tan^{5} (x) sec^{4} (x) d x

What is the integral from 0 to 3 of pi(4sqrt(3y))^2 ?
The integral from 0 to 3 of pi(4sqrt(3y))^2 is pi216