In 512, use Stokes theorem to evaluate C F d r. Assume C is oriented counterclockwise as viewed from above.

L31 - 4 We now generalize this process: To ﬁnd the area under the curve y = f(x) on [a,b]: Divide [a,b]io n subintervals using partition a = = b This creates n subintervals: Then consider n rectangles, one for each subinterval: Width ∆x = Height: f(x i, where x ii Area A can be approximated by the sum of the areas of the n rectangles: This sum is called a Riemann sum.