Originally Posted by
TibiSam Hy everyone!
I don't know exactly how to use some symbols here, but i will denote with int(function) as being the integral of a function.
So I have 4 problems, each of them will be very helpful if you can give a suggestion somehow...
1) lim (n tends to infinity) of n^2 * ∫∫((x^2-y^2)/4)^n dx dy.
The first integral is defined from 0 to 1 (and the variables is y, and the second from y to 2-y and the variable is x).
There is also a hint given: change variables by rotating the axes through an angle of pi/4.
2) ∫∫e^(2x-x^2) dx dy. The first integral is defined from 0 to 1 and the variable is y, the second is defined from 0 to 1-y(1/3) and the variable is x.
3) ∫ 1/((1+x^2)*(1+x^a)) dx, where a is a constant. The integral is defined from 0 to infinity, and the variable is x.
4) ∫f * (x-1/x) dx, where f is a probability density function, the integral is defined from minus infinity to plus infinity and the variable is x.
Thank you a lot if you manage to help me somehow.