0-r-1-r-2-x-2-dx-

Question Number 185471 by liuxinnan last updated on 22/Jan/23

\int_{0}^{r} \frac{1}{\sqrt{r^{2} - x^{2}}} d x = ?

Answered by hmr last updated on 22/Jan/23

Missing \left or extra \right

= ({s i n}^{- 1} (\frac{r}{r})) - ({s i n}^{- 1} (\frac{0}{r}))

= \frac{π}{2} - 0 = \frac{π}{2}

Answered by mr W last updated on 22/Jan/23

l e t x = r \sin θ

d x = r \cos θ d θ

I = \int_{0}^{\frac{π}{2}} \frac{r \cos θ d θ}{r \cos θ} = \int_{0}^{\frac{π}{2}} d θ = \frac{π}{2}

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