Hi there. I'm having some trouble with some double integrals here. All of them are to be evaluated on the rectangle[itex]_{}[/itex] [itex]1≤x≤2, 0≤y≤1[/itex], and the functions are:(adsbygoogle = window.adsbygoogle || []).push({});

1:[itex]\int\int_{A}\frac{1}{x+y}dxdy[/itex].

On this one I made [itex]α(y)=\int^{2}_{1}\frac{1}{x+y}dx=ln(\frac{2+y}{1+y})[/itex], and finally I should evaluate [itex]\int^{1}_{0}α(y)dy[/itex], and this is where I got stuck.

2:[itex]\int\int_{A}xcos(xy)dxdy[/itex].

I again have evaluated [itex]α(y)[/itex], using integration by parts, but then I got stuck with some integrals like [itex]\int\frac{sin(y)}{y}dy[/itex], [itex]\int\frac{cos(2y)}{y^{2}}dy[/itex], and so on, which I couldn't find the primitive.

Any tips on how to evaluate those?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Integral of xcos(xy) over a rectangle

**Physics Forums | Science Articles, Homework Help, Discussion**