Here is a problem I use in my Intro to CS class (lasacs.com/cp) that uses definite integrals.
Thanks for sharing @rmueller ! Looks like a pretty nice and simple introduction to numerical integration.
There should be tons of interesting science problems you can solve with just numerical integration so we’ll definitely try to find something. I know people have been asking for some easier problems so I’m trying to think of a way of introducing the problem as just summing the areas of a bunch of rectangles.