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

The integral from 0 to 5 of pi(2sqrt(5y))^2 is pi250

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

\int_{0}^{5} π (2 5 y)^{2} d y

π 250

Decimal Notation

785.39816 \dots

Solution steps

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

Apply Integration By Parts

: [20 y^{2} - \int 20 y d y]_{0}^{5}

= π [20 y^{2} - \int 20 y d y]_{0}^{5}

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

= π [20 y^{2} - 10 y^{2}]_{0}^{5}

Simplify

= π [10 y^{2}]_{0}^{5}

Compute the boundaries:

250

= π 250

\int \frac{e ^{x}}{36 - e ^{2 x}} d x

\int x 2 - x d x

\frac{d}{d x} (\frac{2 x - 1}{x ^{2} + 1})

x \to 2 lim (\frac{0}{x - 2})

What is the integral from 0 to 5 of pi(2sqrt(5y))^2 ?
The integral from 0 to 5 of pi(2sqrt(5y))^2 is pi250