Line Integral Homework: Solving Problems with W = F*dr and Pictures

Erbil
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Homework Statement



Given by picture.

Homework Equations



W = F*dr

The Attempt at a Solution



Given by pictures.
 

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You should really say what your question about the problem is. And providing less blurry snapshots would really help. If the question is 'where did I go wrong' it looks to me like it's at the very end. Try and find it. You have a much clearer view of your work than I do.
 
Ok.You're right.I will try to fix my fault.But I don't have any idea about b and c? Can you help me for b and c?
 
Erbil said:
Ok.You're right.I will try to fix my fault.But I don't have any idea about b and c? Can you help me for b and c?

c is just two straight line paths. What's a line equation for each part? And if you want a circular path it's probably easiest to use trig functions to describe it. Can you give a parametric form for the circle using cos and sin? BTW I think you are also integrating backward in part a). You want to go from (1,0) to (0,1), not the other way around.
 
Last edited:

Thread 'Prove that the integral is equal to ##\pi^2/8##'

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...
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