October 10th, 2010, 08:10 PM  #1 
Newbie Joined: Oct 2010 Posts: 1 Thanks: 0  Integration requiring Riemann sum
I'm a computer science major and I am currently working on a paper involving GPU programming using CUDA. The cool thing about CUDA is it allows a programmer to do mathematical and scientific calculations at much greater speeds then when using the CPU for calculations. Anyway, I am comparing the speed difference in calculating integrals using Riemann's sum on both the GPU and CPU. I thought it'd be fun to include some examples of integration that requires an approach like Riemann's sum. In other words equations that can't be solved, or at least not easily, using something like antiderivatives. However, I know equations like that exist but it has been so long since I was in calculus I don't remember any examples. Can anyone give me some ideas? Thanks 
October 10th, 2010, 08:26 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: Integration requiring Riemann sum
One expression that immediately springs to mind that does not have an antiderivative expressible in elementary terms is the probability density function for standard normal distribution: ?(x) = (1/?(2?))e^(½x²) 

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