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!

Homework Help: Line Integral

  1. Nov 29, 2012 #1
    1. The problem statement, all variables and given/known data
    Evaluate the line integral ∫(x+2y)dx+(x^2)dy, where C consists of the line segments from (0,0) to (2,1) and (2,1) to (3,0)

    2. Relevant equations

    3. The attempt at a solution

    I'm unsure of what to do. I did (1-t)r0 + t(r1) for (0,0) to (2,1) and (2,1) to (3,0). I didn't get the answer, which is 5/2 however.
  2. jcsd
  3. Nov 29, 2012 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Show us your work and we will help you find what went wrong.
  4. Nov 29, 2012 #3
    Honestly, I have no idea what to do, but here what I did.

    From (0,0) to (2,1)
    r(t) = (1-t)<0,0> + t<2,1>
    r(t) = <2t,t>


    I found that the integral is from 0 to 1.

    dx/dt = 2
    dy/dt = 1

    Then I set x as 2t and y as t into the equation:

    = 4t^2 +4/3t^3 ] <-----evaluate from 0 to 1
    = 4 + 4/3
    = 16/3

    Then I did this same thing for the from (2,1) to (3,0) and added the two numbers.
  5. Nov 29, 2012 #4


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    I agree with 16/3, and I applied the same method for the second segment to get a total of 5/2. So your mistake must be in working you have not posted.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook