Title: What is the integral of √(a-y) /√y Post by: Rentz on Feb 6, 2019 What is the integral of √(a-y) /√y
Title: Re: What is the integral of √(a-y) /√y Post by: bio_man on Feb 6, 2019 Is it with respect to y or a?
Let's assume it's with respect to y, the answer is: Here's how, you have to perform trigonometric substitution: First set u = √y \(2\int \sqrt{a-u^2}du\) Then set \(u=\sqrt{a}\sin \left(v\right)\rightarrow v=\sin ^{-1}\left(\frac{u}{\sqrt{a}}\right),\ \frac{du}{dv}=\sqrt{a}\cos \left(v\right)\) Then solve for du. \(=\int \sqrt{a}\cos \left(v\right)\cdot \sqrt{a-a\sin ^2\left(v\right)}dv\) Simplify: \(a-a\sin ^2\left(v\right)=a\cos ^2\left(v\right)\) \(=a\int \cos ^2\left(v\right)dv\) . . . |