MATH138 Study Guide - Midterm Guide: Arc Length, Trigonometric Substitution, Integral Symbol

• School: University of Waterloo
• Department: Mathematics
• Course: MATH138
• Professor: All

Document Summary

Partial fractions are useful for evaluating ()(), where () and () are polynomials. *need the degree of () to be less than the degree of () (or else do long division) Idea: break up complicated integrals into many easy integrals. A repeated irreducible quadratic (1 +1)(2 +2) ( +) (12 +1 +1) (2 + +) (2 + +) 1 +1 (2 + +) (12 +1 +1) 2 + + + + (2 + +) 3 + 1 ( 1)2 + + ( 1) ( 1)2(2 + 1)2 = (2 + 1)2 (2 + 1) Regular substitution or complete square and trigonometric substitution ( + 1)3(2 + 7)2. 2 + + + (2 + +) = (2 + +) 3. + 3 =3 + 9 +2 + 9 +3 +2. 2 = ln|2 + 9| + ln || + = 5 + 6 =( + 2) +( + 1) Two questions in one, first integral and then limit.