MATH 181 Study Guide - Final Guide: Specific Weight, Farad, Trapezoidal Rule
Document Summary
Problem 1 solution: compute the inde nite integral: Solution: we evaluate the integral using the u-substitution method. 2 dx 2 du = dx and x = 2u and we get: x. 4 x2 (2 du) du du du. Problem 2 solution: consider the curve y = L =z b a s1 +(cid:18) dy dx(cid:19)2 dx where dy. Nd the length of the curve is dx = ( 1. 2 x2) = x, a = 0, and b = 1. 0 (b) we now use the trapezoidal rule with n = 1 to estimate the value of the integral. [f (0) + f (1)] where f (x) = 1 + x2 and the value of x is: Problem 3 solution: show whether the integral below diverges or converges. If it converges, nd the value of the integral: Solution: we evaluate the integral by turning it into a limit calculation. We use the u-substitution method to compute the integral.
