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!

How to integrate modulus function ( absolute value) within the specified limits

  1. Nov 21, 2011 #1
    1. The problem statement, all variables and given/known data

    integrate modulus of xcos∏x within the limits -1 to 1/2

    P.S I'm not allowed to use acaluculator so graphing and finding out the answer not possible
    2. Relevant equations

    it's using the property of definite integral
    ∫f(x) dx within the limit from a to b = ∫f(x) dx within the limit from a to c + ∫f(x) dx within the limit from c to b

    3. The attempt at a solution

    i tried the problem but i don't know how to split the limits..,i.e, how to find c
     
  2. jcsd
  3. Nov 21, 2011 #2

    Deveno

    User Avatar
    Science Advisor

    where is xcos(πx) non-negative?

    split your interval into 4 regions:

    where x < 0 and cos(πx) < 0
    where x < 0 and cos(πx) ≥ 0
    where x ≥ 0 and cos(πx) < 0
    where x ≥ 0 and cos(πx) ≥ 0

    (it may be that some of these regions are empty).

    then integrate the appropriate integrand for each of the (up to) 4 regions.

    for example, on a region where x is negative and the cosine is positive,

    you want -∫f
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: How to integrate modulus function ( absolute value) within the specified limits
Loading...