MATH 141 Midterm: MATH141 BOYLE-M FALL2002 0311 MID EXAM 1

• School: University of Maryland
• Department: Mathematics
• Course: MATH 141
• Professor: All

Document Summary

5x (x 2)(x 3) dx (b) (20 points) z tanx cos3x dx: (20 points) compute the following integral. Z x5ln(x) dx (b) (5 points) the trapezoidal rule for approximating r b a f (x)dx is built out of locally linear approximations to the function f . What kinds of local approximations to f are used to build up the left endpoint and simpson"s rules? a f (x)dx and a f (x)dx|. Suppose that the error estimate for simpson"s rule (c) (5 points) let sn denote the simpson"s rule estimate for a given r b let en = |sn r b shows e10 1. How big should n be to guarantee en . 000 000 01 : (15 points) for each integral below, give the appropriate description: ; ; Dne (does not exist); or converges (i. e. the improper integral is well de ned and converges to a nite real number you don"t have to compute it).