What is the integral from 0 to 20 of pi(sqrt(x))^2 ?

The integral from 0 to 20 of pi(sqrt(x))^2 is pi200

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integral from 0 to 20 of pi(sqrt(x))^2

\int_{0}^{20} π (x)^{2} d x

π 200

Decimal Notation

628.31853 \dots

Solution steps

\int_{0}^{20} π (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}^{20} (x)^{2} d x

Simplify

(x)^{2} : x

= π \cdot \int_{0}^{20} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{0}^{20}

= π [\frac{x ^{2}}{2}]_{0}^{20}

Compute the boundaries:

200

= π 200

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What is the integral from 0 to 20 of pi(sqrt(x))^2 ?
The integral from 0 to 20 of pi(sqrt(x))^2 is pi200