MATH 1014 Study Guide - Midterm Guide: Trapezoidal Rule, Partial Fraction Decomposition, And1

• School: York University
• Department: Mathematics and Statistics
• Course: MATH 1014
• Professor: All

Document Summary

Math 1014 3. 00 pw applied calculus ii prof. madras. Solutions for practice test #1: (a) integrate by parts: let u = ln x and dv = x. Then du = (1/x) dx and v = 2x1/2, and we get(cid:90) ln x dx = 2x1/2 ln x (cid:90) 2x1/2 1 dx x. = 2x1/2 ln x 4x1/2 + c . x (b) use partial fractions. 3x + 4 (x 2)(x + 3) = ax + 3a + bx 2b (x 2)(x + 3) Matching coe cients gives a + b = 3 and 3a 2b = 4. The solution of this pair of equations is a = 2 and b = 1. So (cid:90) x + 3 dx = 2 ln|x 2| + ln|x + 3| + c. (x 2)(x + 3) dx = (cid:90) 1: let x = tan t. then dx = sec2 t dt, and (cid:90) x2.