Math 362 Homework 6 (due Thurs Feb 25) 1. Calculate the following line integrals (a) xdy + ydx, where C is straight line segment connecting (1, 1) to C (0, 0). (b) xdy + ydx where C is the circle of radius 1 centered at the origin, C going once around counterclockwise. (c) (d) C F ds, where C is the same as in (a) and F = ex i + yj F ds, where C is the square consisting of line segments (0, 0) to C (1, 0) to (1, 1) to (0, 1) back to (0, 0), and F = xi + j 2. Find the deriviative f (x) for (a) f (x) = (b) f (x) = (c) f (x) = (d) f (x) = x t e cos t2 dt 0 1 t e cos t2 dt x x et cos t2 dt x 1 cos(xt)dt 0 3. The mean value theorem says that if f (x) is continuous and an interval b [a, b], then there exists c [a, b] such that f (c)(b a) = a f (x)dx. Find a c (if there is a solution) for (a) f (x) = x2 , a = 1, b = 2. (b) f (x) = cos x, a = 0, b = /2. (c) f (x) = a = 1, b = 1 1 0 10 if x < 0 if x 0