× Didn't find what you were looking for? Ask a question
Top Posters
Since Sunday
d
4
N
3
3
R
3
k
3
o
3
Z
3
j
3
s
3
d
3
J
3
1
3
New Topic  
Rentz Rentz
wrote...
5 years ago
What is the integral of √(a-y) /√y
Read 177 times
1 Reply

Related Topics

Replies
wrote...
Educator
5 years ago
Is it with respect to y or a?

Let's assume it's with respect to y, the answer is:

\(\sqrt{a}\sqrt{y}\sqrt{1-\frac{y}{a}}+a\arcsin \left(\frac{\sqrt{y}}{\sqrt{a}}\right)\)

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:

\(a-a\sin ^2\left(v\right)=a\cos ^2\left(v\right)\)

\(=a\int \cos ^2\left(v\right)dv\)

.
.
.
New Topic      
Explore
Post your homework questions and get free online help from our incredible volunteers
  1583 People Browsing
Related Images
  
 207
  
 192
  
 182
Your Opinion
What's your favorite coffee beverage?
Votes: 303