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Changing limits of integration question

  • Thread starter Pyroadept
  • Start date
  • #1

Homework Statement


[tex]\int[/tex](Acosx + Bsinx + C)/(acosx + bsinx +c) dx

where the limits of integration are -π and π

Homework Equations

The Attempt at a Solution

Hi everyone,

My question is: is the function periodic (I'm guessing it is, as it's a combination of sin, cos and constants?)
and, if so, is its period 2π (as sin and cos are of period 2π
and, if so, can we change the limits of integration to 0 and 2π without changing anything else (this would make sense to me)?

Can we do this in general for periodic functions - shift the limits of integration on by a certain number if they are the period?

Thanks for any help

P.S. I know you're supposed to show your work, but I can't really think what else to say!

Answers and Replies

  • #2
These are some easy functions you might want to check out first, in order to understand your own questions.
to your first question: sin(x)+sin(pi*x) 's period=? . by the way, f is period iff f(x)=f(x+T) for some T.
to your second: sin(x)/cos(x)=tan(x)'s period=?
to your third: the denominator can be zero for some x, and therefore I guess you might not be able to integrate it over an arbitrary interval. for example, tan(x) is not integrable over [0,pi/2)