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What are the rules to know when to use absolute value?

  1. Sep 19, 2015 #1
    Specifically when doing integration problems. I know the indef integral of cosx/sinx+1 is ln(sinx+1) + C, but absvalue is not required here. I think it's because the sine fn must be >= 0 or it's undefined? What about in other cases, is there a general rule to know when to use absvalue?

    Thanks
     
  2. jcsd
  3. Sep 19, 2015 #2

    Mark44

    Staff: Mentor

    The integrand should be written as cosx/(sinx + 1). Without parentheses what you wrote is ##\frac{cosx}{sinx} + 1 = cotx + 1##.

    Also, ##\int \frac{\cos(x) dx}{\sin(x) + 1} = \ln|\sin(x) + 1| + C##
    You really should have it, unless there is information given that it's not needed.
    No, that's not true. ##-1 \le \sin(x) \le 1##. Take a look at a graph of y = sin(x).
     
  4. Sep 19, 2015 #3
    I see. So the answer SHOULD have it. We actually don't use a book, so the answers I find to the worksheet problems aren't consistent. Some use absvalue and some do not.

    There definitely should be a parenthesis around the denominator there. I am aware, but neglected it!

    Thanks
     
  5. Sep 20, 2015 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    [itex]\int \frac{1}{x}dx= ln|x|+ C[/itex]. If you know that x will not be negative then you do not need the absolute values.

    For example, [itex]\int_1^2 \frac{1}{x}dx= \left[ln(x)\right]_1^2= ln(2)[/itex]. Since x runs between 1 and 2, it is never negative and the absolute value is not needed.
     
    Last edited by a moderator: Sep 20, 2015
  6. Sep 20, 2015 #5

    Mark44

    Staff: Mentor

    In fact, there should be two of them -- parentheses -- not just a single parenthesis. :oldbiggrin:
     
    Last edited: Sep 20, 2015
  7. Sep 20, 2015 #6
    Yeah, one set around the the angle of sine too.
     
    Last edited by a moderator: Sep 20, 2015
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