MATH 101 Study Guide - Final Guide: Rational Number, Improper Integral, Centroid
Document Summary
Be sure that this examination has 12 pages including this cover. Integral calculus with applications to physical sciences and engineering. Full marks will be awarded for a correct answer placed in the box. Each question is worth 3 marks, but not all questions are of equal difficulty. (a) evaluate 2. Page 3 of 12 pages (d) let k be a positive constant. Find the average value of the function f(x) = sin(kx) on the interval [0, /k]. Answer (e) a function f(x) is always positive and satisfies f (x) = xf(x) for all x and also f(0) = e. Answer (f) find the y-coordinate of the centroid of the region bounded by the curves y = 1, y = ex, x = 0, and x = 1. You may use the fact that the area of this region equals e. Page 4 of 12 pages (g) let rn = integral. n i=1 iei/n n2 .
