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MD5 Hash : 158fb5ebd8719b4f5330b75325e456db
Description : Systemcare Ultimate 8 now supports Windows 10!
Systemcare Ultimate 8 now supports Windows 10!Q:
Homework questions on Differential Geometry
I am currently doing some computer experiments on Differential Geometry and I have some questions :
1)
$$ \iint_R\Big[\frac {x^3-6x+4}{x^2-x+1} -\frac {x-2}{(x-1)^2}\Big]dxdy$$
I have no idea how to approach the problem, is there any formula to solve it?
2) The above integral has two solutions x = 1 or x = 0 for equation $y^2 = x(x-1)$
why is this?
Thanks!
A:
$
ewcommand{\Reals}{\mathbf{R}}
ewcommand{\Cpx}{\mathbf{C}}$The given integral is $$\begin{align*} \iint_R\left(\frac{x^3-6x+4}{x^2-x+1} — \frac{x-2}{(x-1)^2}\right)\,dx\,dy&=\iint_R \frac{x^3-6x+4}{x^2-x+1}\,dx\,dy — \iint_R\frac{x-2}{(x-1)^2}\,dx\,dy\tag{1}\\ &=\int_0^1 \frac{1}{x}dx-\int_1^2 \frac{2}{x-1}\,dx\tag{2}\\ &=\frac{\ln 2}{2}.\tag{
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