What is the integral from 0 to 3 of pi(4sqrt(5x))^2 ?

The integral from 0 to 3 of pi(4sqrt(5x))^2 is pi360

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integral from 0 to 3 of pi(4sqrt(5x))^2

\int_{0}^{3} π (4 5 x)^{2} d x

π 360

Decimal

1130.97335 \dots

Solution steps

\int_{0}^{3} π (4 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}^{3} (4 5 x)^{2} d x

Apply Integration By Parts

= π [80 x^{2} - \int 80 x d x]_{0}^{3}

\int 80 x d x = 40 x^{2}

= π [80 x^{2} - 40 x^{2}]_{0}^{3}

Simplify

= π [40 x^{2}]_{0}^{3}

Compute the boundaries:

360

= π 360

What is the integral from 0 to 3 of pi(4sqrt(5x))^2 ?
The integral from 0 to 3 of pi(4sqrt(5x))^2 is pi360