$\int\frac {dx}{\sqrt{2ax−x²}}=a^n \sin^{-1}(\frac {x}{a}-1)$

Question

The question is telling us to find n The options are: a) 0 b) -1 c) 1 d) none of these I have tried to solve this by using some general formula of integration yet Iam unable to find the answer

@A studious student: Can you show the steps of what you have tried? — Harish Chandra Rajpoot, Jul 02 '20 at 11:37
The proposed answer are numerical, but the integral is indefinite !? — , Jul 02 '20 at 11:43

score 1 · Accepted Answer · answered Jul 02 '20 at 11:16

1

Hint:$$\sqrt{2ax-x^2} =\sqrt{a^2-(x-a)^2}$$ Also, $$\int\frac {dx}{\sqrt{A^2-x^2}}=\sin^{-1}\frac xA+C$$ Now, can you continue from here?

answered Jul 02 '20 at 11:16

$\int\frac {dx}{\sqrt{2ax−x²}}=a^n \sin^{-1}(\frac {x}{a}-1)$

1 Answers1