Proof help! integration -

[marthadowding]

please may someone give me some help with this please!
Sorry if its really simple i just dont really know what theyre asking for??
thank you very much!!!

 

[Deleted member 4993]

View attachment 9509please may someone give me some help with this please!
Sorry if its really simple i just dont really know what theyre asking for??
thank you very much!!!

You are being asked:

If y =\(\displaystyle \sqrt{ r^2 - x^2}\)

(a) \(\displaystyle \frac{dy}{dx} = ? \)

(b) Show that:

\(\displaystyle \displaystyle{\int_{-r}^{+r} \dfrac{r}{\sqrt{r^2-x^2}dx}}\) ......(*)

To do this,

simply replace the expression for dy/dx [found above in (a)] into the definition of L (found in the original question) and simplify algebraically.

c) replace 'x' by rcos(Θ) in the expression (*), along with dx and the limits and perform the integration.

Please share your work with us so that we can help you further.