Changing limits of integration

[dalarev]

[SOLVED] Changing limits of integration

Homework Statement

Given:

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

Change the order of integration and evaluate the double integral.

Homework Equations

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

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".

 

[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.

 

[dalarev]

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.

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.

 

[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.

 

[dalarev]

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