hard calculus?

Question

how do I find the mass of a plate(bounded by 2 curves and the x-axis) with a non-constant density

Answer 1

The element of area in a plane is dy*dx. The element of mass will be d(x,y)*dy*dx, where d(x,y) is the density as a function of x and y.. You are given curves that should be expressed as y = f(x); therefore dy = f'(x)*dx and the mass integral becomes

M = ∫∫d[x,f(x)]*f'(x)dx^2

If you are given two curves, the integral should be done in two parts; the integrals' limits will depend on where the curves intersect the x and y axes.