Math 122 - Fall 2017 - Homework - Chapter 6 Give complete, well written solutions to the following exercises: sh is ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m 1. (30 points) Evaluate the following integrals. Indicate the technique(s) used. Z Z 1 sin x cos x ln x (a) dx dx (d) 4 4 sin x + cos x x 0 Z Z 1 2 (b) dx (e) (2x2 + 1)ex dx x+1+ x Z 3 Z x + 6x2 + 3x + 6 4x (c) dx (f) e e2x + 1 dx x3 + 2x2 2. (5 points) The width, in feet, at various points along the fairway of a hole on a golf course is given in the figure below. If one pound of fertilizer covers 200 square feet, estimate the amount of fertilizer needed to fertilize the fairway. Th 3. (15 points) The probability density function for the standard normal distribution, the familiar bell-shaped curve, is given by the function 1 2 f (x) = ex /2 . 2 Z (a) Show that f (x) dx is convergent. (b) The area under f (x) from x = 1 to x = 1 represents the probability that a normal random variable is within one standard deviation of the mean. Use Simpson's rule (n = 20) to approximate this probability. (c) How accurate is the probability you calculated in part (b)? https://www.coursehero.com/file/25282925/Ch6pdf/ Powered by TCPDF (www.tcpdf.org)