Question

find the value of n............

Answer 1

$I=\int \frac{dx}{\sqrt{2ax-x^2}}\\=\int \frac{dx}{\sqrt{a^2-a^2+2ax-x^2}}\\=\int \frac{dx}{\sqrt{a^2-(x-a)^2}}\\=\frac{1}{a} \int \frac{dx}{1-(\frac{x}{a}-1)^2}\\\text{Let} u=\frac{x}{a}-1\\\Rightarrow du=\frac{dx}{a}\\\Rightarrow dx=adu\\I=\frac{a}{a} \int \frac{dx}{1-u^2}\\={sin}^{-1}u+C\\={sin}^{-1}(\frac{x}{a}-1)+C\\\Rightarrow n=0$

Answer 2

n =0
hope it helps you