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Homework Help: 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


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    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
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