1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Integral over C of f ds

  1. Sep 27, 2014 #1
    1. The problem statement, all variables and given/known data
    I am asked to find the integral over C of fds given C={r=cos(2t), theta=2t, for 0<=t<=pi/2} and f=xy.

    2. Relevant equations


    3. The attempt at a solution

    I know the integral over C of fds is the integral over C of [fsqrt(r'^2+r^2(theta)'^2)]dt, but I don't know how to convert my function f=xy into a function of t so that I can integrate using the dt. I know x=rcos(theta) and y=rsin(theta), but that doesn't allow me to integrate with respect to t.
     
  2. jcsd
  3. Sep 27, 2014 #2
    You're basically asked to do a weighted line integral. It is similar to finding the length of C (the "line" in question), except, instead of f=1, you have f=xy.

    So, you want to convert x and y to r and θ. Then, r and θ will be expressed in terms of t.

    Do you know how to convert x and y to polar coordinates?

    If you get that far, then you will be able to convert the polar coordinates using the "C={..." statement you gave.
     
  4. Sep 27, 2014 #3
    Perfect! I had converted x and y to polar coordinates but I was getting stuck with theta's and r's! I didn't realize that from how C was defined I could rewrite the r and theta's! Thanks a bunch.
     
  5. Sep 27, 2014 #4
    You're welcome! That was usually my biggest hang-up with vector calculus was realizing the interplay between the functions and their domain, and how the domain of the function could be realized through simple direct substitution (say, x=f(t) and y=g(t) then integrate over t)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted