17.2 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.
You can change the number of quadrilaterals used to approximate the value of the integral using the "n" slider and you can drag the points on the curve to change the curve over which the integral is being calculated. Notice how both these changes affect the value of the integral.