# Limits for double integral over trapezoidal shape

1. Mar 19, 2012

### dva

1. The problem statement, all variables and given/known data
I'm trying to determine the limits for a double integral over a symmetric trapezoid or equilateral triangle. I'm not trying to determine the area, and therefore using symmetry to simplify the integration is not an option. The limits for the integration over the y axis are clearly 0-h(h being the height), and the limits for the x axis should be a function of the base width and slope, but i'm unclear as to how they should be properly posed. advice? (should be a simple solution, but its been several years since I had to do any kind of integration).

2. Relevant equations

3. The attempt at a solution

2. Mar 19, 2012

### QuarkCharmer

Well, suppose we have the line y = 0 (the x axis), We need some other function f(x) that makes another constant line and a slope down to the x axis. I can't think of a function that is constant, and then magically linear and decreasing that isn't a piecewise function. So instead, break it up into two double integrals and add them together? That way you have one part with a function g(x) representing the area of the trapezoid under the flat surface, and then another function f(x) = -Cx + D (where C and D are some constants) that you can use for the second integral as a height.