Geometric interpretation of the line integral
This app illustrates the geometric interpretation of the line integral of a positive valued function $f(x,y)$ over a curve $C$ in the $x-y$ plane. The value of the line integral is the area of the "curtain" hanging down from the surface $z = f(x,y)$ to the curve $C$. The area is here approximated by summing up areas of quadrilaterals constructed from the curve up to the surface.