Download Document
Showing page : 1 of 2
This preview has blurred sections. Sign up to view the full version! View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Instructions: Your homework is in two parts, which you should turn in separately. This is not the same as the week 8 course packet homework. There are too many differences to list them all here; just print out this and use it instead of the course packet homework. Due Wednesday, November 22, in lecture. Week 8 Homework Problems, part A 1 2 Stewart, section 8.1: #1, 2, 9, 15, 23 (omit calculator part), 30 Stewart, section 8.3: #23, 25, 29, 32 Week 8 Homework Problems, part B 3 Let k be greater than 1. a) Write a definite integral for the arclength of y = xk from x = 0 to x = b. Do not try to solve the integral. 3 b) One case when this integral can be easily evaluated is when k = 2 . In that case use a substitution to evaluate the integral and find a formula for the arclength in terms of b. c) Use an inverse trig substitution to find a formula for the arclength in the case when k = 2. d) Use Simpson's Rule with 6 sub-intervals to estimate the arclength in the case when k = 3 and b = 1. 4 Consider a uniform flat plate bounded by the graph of y = 1/(1 + x2 ), the graph of y = -1/(1 + x2 ) and the y-axis. Show that the plate has finite mass, but does not have center of mass at a finite distance. (This means that you could lift up the plate, but you could not balance it!) 5 Find the x-coordinate of the center of mass of the uniform flat plate bounded by the x- and y-axes, the line x = 2 and the curve 1 y= . x2 + 6x + 13 y 2 x 6 The formula for the arc length of a curve given parametrically by (x(t), y(t)), for a t b, is b L= a (x (t))2 + (y (t))2 dt. A path of a point on the edge of a rolli...