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

The integral from 0 to 5 of pi(2sqrt(3y))^2 is pi150

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

\int_{0}^{5} π (2 3 y)^{2} d y

π 150

Decimal Notation

471.23889 \dots

Solution steps

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

Apply Integration By Parts

: [12 y^{2} - \int 12 y d y]_{0}^{5}

= π [12 y^{2} - \int 12 y d y]_{0}^{5}

\int 12 y d y = 6 y^{2}

= π [12 y^{2} - 6 y^{2}]_{0}^{5}

Simplify

= π [6 y^{2}]_{0}^{5}

Compute the boundaries:

150

= π 150

\frac{2 s}{1 + 2 s}

\int \frac{x ^{4} + 2}{x ^{2}} d x

f (x) = x - 3, (7, 2)

\frac{d}{d x} (- \frac{6 x}{y})

\frac{9}{x}

What is the integral from 0 to 5 of pi(2sqrt(3y))^2 ?
The integral from 0 to 5 of pi(2sqrt(3y))^2 is pi150