MATH 181 Study Guide - Final Guide: Improper Integral, Ibm System P, Apache Spark
Document Summary
Solution: the integral is improper because the integrand is unde ned at x = 1. To compute the integral we use the u-substitution method with u = 1 x3. Taking the limit as r 1 we get: Solution: the integral is improper because the upper limit of integration is in nite. We evaluate the integral by turning it into a limit calculation. To compute the integral we use the u-substitution method with u = x2. Taking the limit as r + we get: x dx x4 + 1. 2 arctan(cid:0)02(cid:1) x dx x4 + 1 arctan(cid:0)x2(cid:1)(cid:21) Compute the arclength of the graph of y = 2x3/2 from x = 0 to x = 1. Then 1 changes from 0 to 1, and the upper limit of integration changes from 1 to 10. Compute the arclength of the graph of y = 2x3/2 from x = 2 to x = 3. We now use the u-substitution u = 1 + 9x.
