Evaluate the integral.
1|0 s|0 ( t . sqrt ( t2 + s2 ) dt ds
I hope the way I've written it makes some sort of sense.
The Attempt at a Solution
After getting my head around changing the order of integration I get hit with this question and for some reason am totally stumped.
First idea was to switch the order to leave you differentiating with respect to s first.
Which means your just integrating a fairly simple function?
Then instead of following this through my brain just kept saying substitution, substitution.
Using the original integral given.
Setting: u = t2+s2
du/2 = t.dt
Then substitute in accordingly. But I was confused by how you change the interval values.
With single integration your simply left with something like u = x + 1
I looked around and found to make a substitution you need to create two variables say and u and a v. This got me interested but also slightly more confused.
Writing this out has cleared my head and lead me to believe that the first method could work and I will try it out now.
What I would appreciate is a method on how to solve the integral (if both of mine are wrong), but now mainly an explanation on substitution with two integrals.