What is the integral from 0 to 3 of pi(6sqrt(3y))^2 ?

The integral from 0 to 3 of pi(6sqrt(3y))^2 is pi486

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integral from 0 to 3 of pi(6sqrt(3y))^2

\int_{0}^{3} π (6 3 y)^{2} d y

π 486

Decimal Notation

1526.81402 \dots

Solution steps

\int_{0}^{3} π (6 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} (6 3 y)^{2} d y

Apply Integration By Parts

: [108 y^{2} - \int 108 y d y]_{0}^{3}

= π [108 y^{2} - \int 108 y d y]_{0}^{3}

\int 108 y d y = 54 y^{2}

= π [108 y^{2} - 54 y^{2}]_{0}^{3}

Simplify

= π [54 y^{2}]_{0}^{3}

Compute the boundaries:

486

= π 486

(x^{2} + y^{2}) d x - x y d y = 0

\int \frac{6}{x} d x

\int \frac{1}{( 1 + x ) ^{4}} d x

\int cos (x) e^{2 x} d x

3 y^{^{''}} + 48 y = 0

What is the integral from 0 to 3 of pi(6sqrt(3y))^2 ?
The integral from 0 to 3 of pi(6sqrt(3y))^2 is pi486