# Changing limits of integration question

In summary, the question is asking to evaluate the integral of a function with limits of integration -π and π. The function contains trigonometric functions and constants, and the question also asks if the function is periodic and if its period is 2π. The poster also wonders if the limits of integration can be shifted to 0 and 2π without changing the result, and if this can be done for periodic functions in general. The response to the questions includes examples of other periodic functions and their periods, and a note about the possibility of the denominator being zero and affecting the integrability of the function.

## Homework Statement

Evaluate

$$\int$$(Acosx + Bsinx + C)/(acosx + bsinx +c) dx

where the limits of integration are -π and π

## 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!

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)

## 1. What is a changing limit of integration question?

A changing limit of integration question is a type of problem in calculus that involves finding the new limits when the variables in the integral are changed.

## 2. What is the purpose of changing limits of integration?

The purpose of changing limits of integration is to make it easier to evaluate integrals by transforming the original integral into a simpler form that can be solved more easily.

## 3. How do you change the limits of integration?

To change the limits of integration, you can use a substitution method, such as u-substitution or trigonometric substitution, to transform the variables in the integral. This will result in new limits that can be evaluated more easily.

## 4. When should I use changing limits of integration?

You should use changing limits of integration when you encounter an integral that is difficult to solve with the original limits. By transforming the integral and changing the limits, you can make the problem more manageable.

## 5. Are there any limitations to changing limits of integration?

Yes, there are some limitations to changing limits of integration. In some cases, the substitution method may not work, or it may lead to a more complicated integral. It is important to carefully consider the problem before attempting to change the limits of integration.

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