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Calculate the following line integral

  1. Dec 6, 2016 #1
    1. The problem statement, all variables and given/known data
    Let ##f(x,y)=(xy,y)## and ##\gamma:[0,2\pi]\rightarrowℝ^2##,##\gamma(t)=(r\cos(t),r\sin(t))##, ##r>0##. Calculate ##\int_\gamma{f{\cdot}d\gamma}##.

    2. Relevant equations


    3. The attempt at a solution
    The answer is 0. Here's my work. However, this method requires that you are familiar with some useful trig identities.
    2cpuy6v.jpg

    Could someone please take a look at it and check if it's correct? Are there alternative ways? I have also tried to find the potential function ##u##, ##\nabla{u}=f##...
     
    Last edited: Dec 6, 2016
  2. jcsd
  3. Dec 6, 2016 #2

    Ray Vickson

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    Homework Helper

    I get an answer of 0 as well, but I have not checked your work because I do not look at posted images, but only at typed versions.
     
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