1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Integrating a non-elementary function

  1. Apr 16, 2009 #1
    1. The problem statement, all variables and given/known data

    Integral (pi1/2, 0) of Integral (pi1/2, y) sin(y2) dxdy

    2. Relevant equations

    This one is interesting because it can't be integrated as is (at least not at the level of my course) but I think with some rearranging it can be done. I was wondering if anyone could verify my method.

    BTW, I'm kinda new, so I don't know exactly how to make the little integral symbol. If that's too hard to read, it's a double integral defined on the inside between "y" and the square root of pi, and defined on the outside between 0 and the square root of pi. The function is sin(y2), with dx, then dy. That is, I believe 0 < y < pi1/2 and y < x < pi1/2.

    3. The attempt at a solution

    Alright so as is, it's not an elementary function and cannot be worked with, I believe. I rearranged the "parameters" to define x as 0 < x < pi1/2 and 0 < y < x. Then, "dx" and "dy" switch positions in the original equation, and I integrated sin(y2) with respect to "x" first. Simply put, I got xsin(y2). Then, integrating with respect to "y" by parts, I got xsin(y2) - [(1/2)(x2) * -(2y)(cos(y2))]. Without doing all the math here, I'll tell you I ended up with pi2.

    I feel I got the problem right all the way until the final integration. I'm mostly afraid I messed up the final step in integration. If anyone would like to look at my process, that would be great.

    PS -- if anyone knows how to directly integrate a non-elementary function, that would be cool to see.
     
  2. jcsd
  3. Apr 16, 2009 #2
    Is your integral:


    [tex]\int_{0}^{\sqrt\pi}\int_{y}^{\sqrt\pi}sin(y^2)dxdy[/tex]


    ???

    If this is the integral you are working with then, notice that you are first integrating with respect to x, so you can treat

    [tex]sin(y^2)[/tex] merely as a constant. And after you have integrated with respect to x, you will end up with an integral that can be easily integrated with a u-substitution.
     
    Last edited: Apr 16, 2009
  4. Apr 16, 2009 #3
    Sorry!!! Good point.

    The integral I put was not the original. I rearranged the original to get to that point, so ignore my "process" as that's how I got to the formula above. Thanks.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Integrating a non-elementary function
  1. Non elementary integral (Replies: 12)

Loading...