What is the integral from 0 to 1 of pi(sqrt(x))^2 ?

The integral from 0 to 1 of pi(sqrt(x))^2 is pi/2

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integral from 0 to 1 of pi(sqrt(x))^2

\int_{0}^{1} π (x)^{2} d x

\frac{π}{2}

Decimal

1.57079 \dots

Solution steps

\int_{0}^{1} 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}^{1} (x)^{2} d x

Simplify

(x)^{2} : x

= π \cdot \int_{0}^{1} x d x

Apply the Power Rule

= π [\frac{x ^{2}}{2}]_{0}^{1}

Compute the boundaries:

\frac{1}{2}

= π \frac{1}{2}

Simplify

= \frac{π}{2}

What is the integral from 0 to 1 of pi(sqrt(x))^2 ?
The integral from 0 to 1 of pi(sqrt(x))^2 is pi/2