周次: 7 日期: April 6, 2022 节次: 1 In this lecture, we explore more examples of integration. Trigonometric substitutions and integration by looking up the integration tables are covered. Note that most of these calculations can be done by hands. § 8.5 Three Basic Substitutions The most common substitutions are $x=a\tan\theta$, $a=\sin\theta$, and $x=a\sec\theta$. They can be useful for dealing with the integrals involving...
周次: 6 日期: April 1, 2022 节次: 2 In this lecture, we continue presenting the integration of rational functions. After finishing this part, we are going to discuss some trigonometric integration techniques. Outline § 8.3 Integration of Rational Functions Method of Partial Fractions ( for $f(x)/g(x)$ Proper) Factorize the denominator $g(x)$, obtain all its linear and quadratic factors, as well as their powers. In...
周次: 5 日期: March 23, 2022 节次: 1 In this lecture, we define the inverse trigonometric functions, and develop some basic properties. The properties we are focusing on are the differentiation and integration properties. A brief introduction on hyperbolic functions, in particular the hyperbolic cosine and hyperbolic sine functions are given. As the second half, we discuss some integration techniques. Those techniques could help...