What is the integral from 0 to 5 of pi(2sqrt(7y))^2 ?

The integral from 0 to 5 of pi(2sqrt(7y))^2 is pi350

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integral from 0 to 5 of pi(2sqrt(7y))^2

\int_{0}^{5} π (2 7 y)^{2} d y

π 350

Decimal

1099.55742 \dots

Solution steps

\int_{0}^{5} π (2 7 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 7 y)^{2} d y

Apply Integration By Parts

: [28 y^{2} - \int 28 y d y]_{0}^{5}

= π [28 y^{2} - \int 28 y d y]_{0}^{5}

\int 28 y d y = 14 y^{2}

= π [28 y^{2} - 14 y^{2}]_{0}^{5}

Simplify

= π [14 y^{2}]_{0}^{5}

Compute the boundaries:

350

= π 350

\int_{2}^{\infty} e^{- 9 x} d x

\int \frac{1}{4 x y ^{2}} d x

f (x) = \frac{11 x + 7}{3 x ^{4} + 2 x ^{2}}

\frac{\partial}{\partial x} (\frac{x ^{2} + y ^{2}}{x y})

\frac{\partial}{\partial x} (\frac{y ^{3}}{x})

What is the integral from 0 to 5 of pi(2sqrt(7y))^2 ?
The integral from 0 to 5 of pi(2sqrt(7y))^2 is pi350