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## Homework Statement

Evaluate the integral.

^{1}|

_{0}

^{s}|

_{0}( t . sqrt ( t

^{2}+ s

^{2}) 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 = t

^{2}+s

^{2}

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.

Thanks!

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