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

The integral from 0 to 5 of pi(sqrt(5x))^2 is (125pi)/2

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

\int_{0}^{5} π (5 x)^{2} d x

\frac{125 π}{2}

Decimal Notation

196.34954 \dots

Solution steps

\int_{0}^{5} π (5 x)^{2} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= π \cdot \int_{0}^{5} (5 x)^{2} d x

Apply Integration By Parts

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

= π [5 x^{2} - \int 5 x d x]_{0}^{5}

\int 5 x d x = \frac{5 x ^{2}}{2}

= π [5 x^{2} - \frac{5 x ^{2}}{2}]_{0}^{5}

Join

5 x^{2} - \frac{5 x ^{2}}{2} : \frac{5 x ^{2}}{2}

= π [\frac{5 x ^{2}}{2}]_{0}^{5}

Compute the boundaries:

\frac{125}{2}

= π \frac{125}{2}

Simplify

= \frac{125 π}{2}

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What is the integral from 0 to 5 of pi(sqrt(5x))^2 ?
The integral from 0 to 5 of pi(sqrt(5x))^2 is (125pi)/2