Homework Help: Changing limits of integration

1. Mar 17, 2008

dalarev

[SOLVED] Changing limits of integration

1. The problem statement, all variables and given/known data

Given:

$$\int_{y=0}^\pi\int_{x= y}^{\pi}\frac{sinx}{x} dxdy$$

Change the order of integration and evaluate the double integral.

2. Relevant equations

My professor told me, "This integral cannot be expressed in terms of elementary functions". I'm not exactly sure what that means.

3. The attempt at a solution

sinx/x has always been a very common problem for differentiation and integration, so I'm confident I can solve this with a simple substitution. I'm trying to figure out, however, what they mean by not being able to be expressed in terms of "elementary functions".

2. Mar 17, 2008

Vid

The integral of sin(x)/x can't be done by any solution. It can't be expressed as a sum or product or quotient of any of the functions you see in calculus. Changing the limits to integrate with y first will allow you to actually do the integral.

3. Mar 17, 2008

dalarev

So I assume representing sinx/x graphically, and then choosing the correct y limits is all their is to this problem? I'm at work, just trying to get a head start on this problem.

4. Mar 17, 2008

Vid

f(x,y) = sin(x)/x is a 2d- surface. Graph the limits, not the function. Then reverse the order so that y is a function of the x in the first integral.

5. Mar 17, 2008

dalarev

Ok, I see it, will mark as solved. Thanks for the help.