What is the integral of pi(sqrt(x))^2 ?

The integral of pi(sqrt(x))^2 is (pix^2)/2+C

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integral of pi(sqrt(x))^2

\int π (x)^{2} d x

\frac{π x ^{2}}{2} + C

Solution steps

\int 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 (x)^{2} d x

Simplify

(x)^{2} : x

= π \cdot \int x d x

Apply the Power Rule

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

= π \frac{x ^{2}}{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{π x ^{2}}{2}

Add a constant to the solution

= \frac{π x ^{2}}{2} + C

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\int 49 e^{- 7 x} sin (7 x) d x

\frac{\partial}{\partial x} (cos (6 y - 2 x))

What is the integral of pi(sqrt(x))^2 ?
The integral of pi(sqrt(x))^2 is (pix^2)/2+C