What is the integral of sqrt(3r^2) ?

The integral of sqrt(3r^2) is (sqrt(3)r^2)/2+C

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integral of sqrt(3r^2)

\int 3 r^{2} d r

\frac{3 r ^{2}}{2} + C

Solution steps

\int 3 r^{2} d r

Apply radical rule:

n ab = n a n b,

assuming

a \geq 0, b \geq 0

= \int 3 r^{2} d r

Take the constant out:

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

= 3 \cdot \int r^{2} d r

r^{2} = (r),

assuming

r \geq 0

= 3 \cdot \int r d r

Apply the Power Rule

: \frac{r ^{2}}{2}

= 3 \frac{r ^{2}}{2}

Multiply fractions:

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

= \frac{3 r ^{2}}{2}

Add a constant to the solution

= \frac{3 r ^{2}}{2} + C

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What is the integral of sqrt(3r^2) ?
The integral of sqrt(3r^2) is (sqrt(3)r^2)/2+C