MATH100 Chapter Notes - Chapter 7: Improper Integral, Ibm Aix

• School: University of Alberta
• Department: Mathematics
• Course: MATH100
• Professor: Meymanat Farzamirad

Document Summary

7. 1 integration by parts: formula for integration by parts: Chapter 7 techniques of integration: alternative notation: If we combine the formula for integration by parts with part 2 of the fundamental. Theorem of calculus, we can evaluate definite integrals by parts: 7. 4 trigonometric substitution: table of trigonometric substitutions, hyperbolic substitutions can be used in place of trigonometric substitutions and sometimes they lead to simpler answers. , then we must take the preliminary step: four cases, case i the denominator is a product of distinct linear factors. We can write: case ii q(x) is a product of linear factors, some of which are repeated. Suppose the first linear factor is repeated r times, we would us: case iii q(x) contains irreducible quadratic factors, none of which is repeated. The expression for r(x)/q(x) will have a term of the form. It can be integrated by using the formula: case iv q(x) contains a repeated irreducible quadratic factor.