MATH 181 Study Guide - Final Guide: Trapezoidal Rule, Irreducible Fraction
Document Summary
Problem 1 solution: compute the following integrals. dx (a) ! (b) ! sin x dx. Solution: (a) the integral is computed using the u-substitution method. Let u = 1 2 cos x. Substituting these into the integral and evaluating du = 2 sin x dx we get: 1 2 cos x dx = ! 2 ln |1 2 cos x| + c (b) the integral is computed using the u-substitution method. 2 du = dx and we get: dx. 1 arcsin u + c du arcsin(2x) + c. Problem 2 solution: find the volume of the solid of revolution obtained by rotating the region in the rst quadrant bounded by y = x2, x + y = 6, and x = 0 about the y-axis. To nd the volume we will use the shell method. The variable of integration is x and the formula is: x (top bottom) dx.
