Advanced Math Puzzle

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Some problems occured,will solve them in 10 minutes

Edit: Problems solved!

Ok since i cannot embed images i have them on a link

I think we are ready to start

I regret when I skipped math class.

Integration solved in 5 seconds but I don't know how to solve others. :/

Integral I of K meaning, specifically, what? Should I find I(z) = int(f(z)dz) (in the first img)? int(K(x)dx)? Some superposition? K(I(z)) (then the coordinates are messed up)

When you say below the curve, do you mean the curve itself? You don't mean the infinite area under the curve CDE right?

No idea at all.

I first thought this was exactly what I learned from school last year.
But after some attempts and research, it looks like this is way beyond what I learned. O.o
Is this supposed to be a very difficult integral problem? Is Cauchy involved here?

Engineers are gods, they do this sort of stuff for a living. I can't stand math and forgot pretty much everything when I first had the chance. Nice way to put it all, by the way.

I might have reached an answer, but I have no idea in which form should I enter it.

Latest I took was calculus, so, I'm stumped after the integral.

Line integral ftw. Too bad it's not a closed loop. Really wish I paid more attention when they taught complex analysis.

Where is my mind?

Is the polar curve in the complex plane?

How much time do we have to solve it?

I need some refreshment on how to do this type of integrals. Heh...

Why I read it Advanced Meth Puzzle, I don't know, but I am disappointed now :(

Bump

8 entries so far with 4 days left :)

1 day and some hours left

10 entries so far!