What is the integral from 0 to r of sqrt(r^2-r^2)r ?

The integral from 0 to r of sqrt(r^2-r^2)r is 0

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integral from 0 to r of sqrt(r^2-r^2)r

\int_{0}^{r} r^{2} - r^{2} r d r

0

Solution steps

\int_{0}^{r} r^{2} - r^{2} r d r

Simplify

= \int_{0}^{r} 0 d r

Integral of a constant:

\int a d x = a x

= [0 \cdot r]_{0}^{r}

Simplify

= [0]_{0}^{r}

Compute the boundaries:

0

= 0

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What is the integral from 0 to r of sqrt(r^2-r^2)r ?
The integral from 0 to r of sqrt(r^2-r^2)r is 0