4
votes
1answer
282 views

Using geometric arguments to solve an analysis problem

Im not good in geometric interpretations... any help is very welcome. Consider the unitary disc $$D=\{(x,y,0)\in\mathbb{R}^3, x^2+y^2\leq1\},$$ parameterized by ...
0
votes
1answer
188 views

parametrizing quarter of a circle

I am given the circle whose equation is: $(x-\frac{1}{2})^{2}+(y+\frac{1}{2})^{2}=\frac{1}{2}$. So, the coordinates of the origin of the circle are: $(\frac{1}{2},-\frac{1}{2})$ and the radius of the ...
3
votes
1answer
321 views

Solving integral equation with Laplace's Transform.

I'm trying to prove the following $$\int\limits_0^\infty {\frac{{\cos tu}}{{{u^2} + 1}}\log udu} = - \frac{\pi }{2}\int\limits_0^\infty {\frac{{\sin tu}}{{{u^2} + 1}}du} $$ The original problem ...