1. Not finding help here? Sign up for a free 30min 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!

Evaluate line integral

  1. Mar 30, 2012 #1

    sharks

    User Avatar
    Gold Member

    The problem statement, all variables and given/known data
    Evaluate [itex]\int3x^2dx+2xydy[/itex], where C is the curve [itex]x^2+y^2=4[/itex] starting at (2,0) and ending at (0,2) in the anti-clockwise direction.

    The attempt at a solution
    The curve C is a quarter-circle with centre (0,0) and radius=2.
    Making y subject of formula:
    [tex]y=+\sqrt{4-x^2}[/tex] since the quarter-circle is above the x-axis.
    [tex]\frac{dy}{dx}=-\frac{x}{\sqrt{4-x^2}}[/tex]
    Replacing y and dy in the line integral.
    [tex]\int3x^2dx+2xydy=\int_{x=2}^{x=0} 3x^2dx+2x.\sqrt{4-x^2}.-\frac{x}{\sqrt{4-x^2}}.dx=\int_{x=2}^{x=0} x^2dx=\frac{x^3}{3}\Biggr|_2^0=(0-\frac{8}{3})=-\frac{8}{3}[/tex]
    Is this correct?
     
  2. jcsd
  3. Mar 30, 2012 #2

    sharks

    User Avatar
    Gold Member

    My friend told me that this problem should be solved by converting to polar coordinates. But i did it directly without any conversion, which is why i'm wondering if it's good at all?
     
  4. Mar 31, 2012 #3

    ehild

    User Avatar
    Homework Helper
    Gold Member

    It is correct.

    ehild
     
  5. Mar 31, 2012 #4

    sharks

    User Avatar
    Gold Member

    Thank you for your confirmation, ehild. :smile:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Evaluate line integral
  1. Evaluate line integral (Replies: 3)

  2. Line Integral Evaluation (Replies: 25)

Loading...