Textbook Guide Mathematics: Integral, Trigonometric Substitution, Trapezoidal Rule
99
MAT133Y1 Full Course Notes
Verified Note
99 documents
Document Summary
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: Strategy for evaluating (a) if the power of secant is even, substitute u = tanx (b) if the power of tangent is odd, substitute u = secx. Hyperbolic substitutions can be used in place of trigonometric substitutions and sometimes they lead to simpler answers. But we usually use trigonometric substitutions because trigonometric identities are more familiar than hyperbolic identities. Sometimes we need to transform the integrand into a function for which trigonometric substitution is appropriate by first completing the square under the root sign. 7. 4 integration of rational functions by partial fractions. We can integrate any rational function (a ratio of polynomials) by expressing it as a sum of simpler fractions, called partial fractions, that we already know how to integrate. A rational function: if f is improper,
