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!

Line integral convert to polar coordinates

  1. May 21, 2016 #1
    1. The problem statement, all variables and given/known data
    I need to find the work done by the force field:
    $$\vec{F}=(5x-8y\sqrt{x^2+y^2})\vec{i}+(4x+10y\sqrt{x^2+y^2})\vec{j}+z\vec{k}$$
    moving a particle from a to b along a path given by:
    $$\vec{r}=\frac{1}{2}\cos(t)\vec{i}+\frac{1}{2}\sin(t)\vec{j}+4\arctan(t)\vec{k}$$
    3. The attempt at a solution
    So I set up my line integral:
    $$\vec{F}(\vec{r}(t))=(\frac{5}{2}\cos(t)-2\sqrt{2}\sin(t))\vec{i}+(2\cos(t)+\frac{5\sqrt{2}}{2}\sin(t))\vec{j}+(4\arctan(t))\vec{k}$$
    $$\vec{r'}(t)=\left(-\frac{1}{2}\sin(t)\right)\vec{i}+\left(\frac{1}{2}\cos(t)\right)\vec{j}+\left(\frac{4}{t^2+1}\right)\vec{k}$$
    $$\int_0^{1}\left(-\frac{5+5\sqrt{2}}{4}\sin(t)\cos(t)+\sqrt{2}\sin^2(t)+\cos^2(t)+\frac{16\arctan(t)}{t^2+1}\right)\; \text{d}t=5.86436$$

    I have left a lot of steps out, it gets messy! Could this problem be solved by reducing the integral to polar coordinates?
     
  2. jcsd
  3. May 21, 2016 #2

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    What makes you think you didn't use polar coordinates to get your result?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted