Question

answer this question:

Integrate the following:
$\\ \int \frac{dx}{ \sqrt{2ax - {x}^{2} } }$
with proper steps and reasoning

Answer 1

Hi friend!!

The solution is given in the following attachment.

I hope this will help you ;)

Answer 2

$= \int\ { \frac{1}{ \sqrt{2ax- x^{2} } } } \, dx$
$= \int\ { \frac{1}{ \sqrt{2ax- x^{2} + a^{2} - a^{2} } } } \, dx$
$= \int\ { \frac{1}{ \sqrt{a^{2} - [x-a] ^{2} } } } \, dx$
=Sin inverse [(x-a)/x]+C