Theory and Applications

A string lies along the circle x2 + y2 = 4 from (2, 0) to (0, 2) in the first quadrant. The density of the string is

a. Partition the string into a finite number of subarcs to show that the work done by gravity to move the string straight down to the x-axis is given by

b. Find the total work done by evaluating the line integral in part (a).

c. Show that the total work done equals the work required to move the string’s center of mass straight down to the x-axis.

Calculus notes for the week of 10/3/16 4.1 Maxima and Minima and 4.2 What Derivatives Tell Us 15 10 5 01 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 -5 -10 -15 f has a local maximum at c if f(c) > f(x) for all x sufficiently close to c. f has a local minimum at c if f(c) < f(x) for all x sufficiently close to c. We see that, if f is differentiable at a local...