- #1
carlosbgois
- 66
- 0
Hi there. I'm having some trouble with some double integrals here. All of them are to be evaluated on the rectangle_{} 1≤x≤2, 0≤y≤1, and the functions are:
1: \int\int_{A}\frac{1}{x+y}dxdy.
On this one I made α(y)=\int^{2}_{1}\frac{1}{x+y}dx=ln(\frac{2+y}{1+y}), and finally I should evaluate \int^{1}_{0}α(y)dy, and this is where I got stuck.
2: \int\int_{A}xcos(xy)dxdy.
I again have evaluated α(y), using integration by parts, but then I got stuck with some integrals like \int\frac{sin(y)}{y}dy, \int\frac{cos(2y)}{y^{2}}dy, and so on, which I couldn't find the primitive.
Any tips on how to evaluate those?
1: \int\int_{A}\frac{1}{x+y}dxdy.
On this one I made α(y)=\int^{2}_{1}\frac{1}{x+y}dx=ln(\frac{2+y}{1+y}), and finally I should evaluate \int^{1}_{0}α(y)dy, and this is where I got stuck.
2: \int\int_{A}xcos(xy)dxdy.
I again have evaluated α(y), using integration by parts, but then I got stuck with some integrals like \int\frac{sin(y)}{y}dy, \int\frac{cos(2y)}{y^{2}}dy, and so on, which I couldn't find the primitive.
Any tips on how to evaluate those?
