Results 1 to 2 of 2

Thread: evaluate the integral

  1. #1
    Senior Member
    Jan 2010

    evaluate the integral

    Let C be the semi circle on the surface $\displaystyle x^2+y^2+z^2=4$ from $\displaystyle N=(0,0,2) $to $\displaystyle S=(0,0,-2)$ which passes through the point ($\displaystyle \sqrt{2}$,$\displaystyle \sqrt{2}$,$\displaystyle 0$) (note that x=y for all (x,y,z) on C.)
    Evaluate the integral
    $\displaystyle \int _c\!z^2dx + 2x^2dy + xydz$

    (Suggestion: use as your parameter the angle Q subtended at the orgin by the arc NP for a point P on C)

    I think i need to sketch the picture to understand it, but Im having a hard time to do it, is there another way to find x,y,z in term of t?
    Last edited by wopashui; Jan 8th 2011 at 06:26 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Dec 2010
    Your semi circle is part of the intersection between the plane x=y and the sphere of radius 2.

    So points on your semicircle satisfy
    $\displaystyle 4 = x^2 + y^2 + z^2 = 2x^2 + z^2 = 2y^2 + z^2$
    Can you find parametric equations for x, y, and z on the semicircle?

    Hint: x = y = Asin(t), z = Bcos(t), what are A,B, and the range for t?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: Aug 31st 2010, 07:38 AM
  2. Replies: 1
    Last Post: Jun 2nd 2010, 02:25 AM
  3. Replies: 1
    Last Post: Nov 28th 2009, 08:44 AM
  4. evaluate the integral
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Jun 19th 2009, 08:27 PM
  5. Evaluate the integral
    Posted in the Math Challenge Problems Forum
    Replies: 3
    Last Post: May 2nd 2009, 07:39 PM

Search Tags

/mathhelpforum @mathhelpforum