What is the integral from-r to r of xsqrt(r^2-x^2) ?

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

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integral from-r to r of xsqrt(r^2-x^2)

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

0

Solution steps

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

If f(x) is an odd function and continuous at:

[- a, a]

then

\int_{- a}^{a} f (x) d x = 0

Parity of

x r^{2} - x^{2} :

Odd

= 0

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