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.
 
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There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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