What is the integral from 0 to 9 of 2pix(sqrt(x)) ?

The integral from 0 to 9 of 2pix(sqrt(x)) is (972pi)/5

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integral from 0 to 9 of 2pix(sqrt(x))

\int_{0}^{9} 2 π x (x) d x

\frac{972 π}{5}

Decimal Notation

610.72561 \dots

Solution steps

\int_{0}^{9} 2 π x x d x

Take the constant out:

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

= 2 π \cdot \int_{0}^{9} x x d x

Simplify

x x : x^{\frac{3}{2}}

= 2 π \cdot \int_{0}^{9} x^{\frac{3}{2}} d x

Apply the Power Rule

: [\frac{2}{5} x^{\frac{5}{2}}]_{0}^{9}

= 2 π [\frac{2}{5} x^{\frac{5}{2}}]_{0}^{9}

Compute the boundaries:

\frac{486}{5}

= 2 π \frac{486}{5}

Simplify

= \frac{972 π}{5}

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What is the integral from 0 to 9 of 2pix(sqrt(x)) ?
The integral from 0 to 9 of 2pix(sqrt(x)) is (972pi)/5