What is the integral from 0 to 4 of pi(sqrt(x)) ?

The integral from 0 to 4 of pi(sqrt(x)) is (16pi)/3

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integral from 0 to 4 of pi(sqrt(x))

\int_{0}^{4} π (x) d x

\frac{16 π}{3}

Decimal

16.75516 \dots

Solution steps

\int_{0}^{4} π x d x

Take the constant out:

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

= π \cdot \int_{0}^{4} x d x

Apply the Power Rule

: [\frac{2}{3} x^{\frac{3}{2}}]_{0}^{4}

= π [\frac{2}{3} x^{\frac{3}{2}}]_{0}^{4}

Compute the boundaries:

\frac{16}{3}

= π \frac{16}{3}

Simplify

= \frac{16 π}{3}

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What is the integral from 0 to 4 of pi(sqrt(x)) ?
The integral from 0 to 4 of pi(sqrt(x)) is (16pi)/3