Solving for u: Struggling with a 2D Homework Problem

dirk_mec1
Messages
755
Reaction score
13

Homework Statement



1.PNG

The Attempt at a Solution



I don't know how to choose u. I presume we look in 2D; I thought u should look something like:

u = \left[ \begin{array}{c} \psi \\ \psi \end{array} \right]

and c= \phi but that isn't correct.
 
Physics news on Phys.org
How about picking two vector fields? Pick u=(psi,0) for the first part and u=(0,psi) for the second part.
 
Dick said:
How about picking two vector fields? Pick u=(psi,0) for the first part and u=(0,psi) for the second part.

Yes of course, thanks Dick!
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
Back
Top