MA101 Study Guide - Final Guide: Partial Fraction Decomposition, Antiderivative
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Ma101 lab report 8 - integrating rational functions and partial fraction. Q(x) where p and q are polynomials (i. e. f is a rational function). Z f (x)dx may be evaluated using a number of techniques, such as: the substitution rule: Used to express the integrand in a form where the general antiderivative is known. We try to make a substitution, say u = g(x), where both g(x) and g (x) are factors in the integrand. = z f (u)du let u = g(x), then du = g (x)dx. Let u = x2 + 4, then du = 2xdx. When x = 0, u = 4 and x = 1, u = 5. 4 = ln 5 ln 4: factoring and cancelling: Z x2 4 x + 2 dx = z (x 2)(x + 2) x + 2 dx. 2x + c: partial fraction expansion: Suppose f is a rational function of the form f (x) =
