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!

Help! u-substitution, new boundaries question

  1. Nov 3, 2011 #1
    what do i do if when i am changing the limits/boundaries on my integral because i did a u substitution and the new limits end up being the same number?

    EXAMPLE:

    integral is of:

    4*(sin(theta)^4)*cos(theta) dtheta

    the limits are pi/6 to 5*pi/6
    i had u= sin(theta) .... both the u lower and upper limits equal 1/2.....

    the original integral was a double integral in polar coordinates... limits of r was o-2sin(theta) and i already stated the theta's limits. the function is (r^3)*cos(theta)

    it doesnt make sense to me to let u=cos(theta) in this case of
    "integral is of:
    4*(sin(theta)^4)*cos(theta) dtheta"
     
  2. jcsd
  3. Nov 3, 2011 #2

    Mark44

    Staff: Mentor

    If you end up with an integral whose limits of integration are the same, the value of your integral is zero.

    An alternate approach involves not changing the limits of integration. First, evaluate the indefinite integral to get an antiderivative of 4sin4(t)cos(t). Then evaluate your antiderivative at the upper and lower limits of integration, and subtract.
     
  4. Nov 3, 2011 #3
    i realized that after i played around with it some more. thanks!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Help! u-substitution, new boundaries question
Loading...