题目

MAT136H5 S 2025 - All Sections 3.4 Preparation Check

多项选择题

Suppose you want to use the method of partial fractions to integrate ∫ P(x) Q(x) dx where P(x) and Q(x) are polynomials. Which of the following statements are TRUE? Select all that apply.

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思路分析

We’re evaluating statements about the algorithm for using partial fractions to integrate a rational function P(x)/Q(x). Option 1: If P(x) = x^4 - x^2 and Q(x) = 3x^4 - 1, then the first step is to use long division. Here the degrees of P and Q are both 4,......Login to view full explanation

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In the partial fraction decomposition 2 𝑥 2 + 5 𝑥 + 9 ( 4 𝑥 + 1 ) ( 5 𝑥 2 + 1 ) = 𝐴 4 𝑥 + 1 + 𝐵 𝑥 + 𝐶 5 𝑥 2 + 1 , what are the values of 𝐴 , 𝐵 and 𝐶 ?

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Calculate the integral $$\int_0^2 \dfrac{x+5}{x^2-2x-3}\, dx$$

Question textThe function f(x)=\dfrac{x+2}{(x+1)(x-1)^2} can be resolved into partial fractions of the form:\dfrac{a}{x+1} + \dfrac{b}{x-1} + \dfrac{c}{(x-1)^2}where a,\,b and c are real number values.Use this to express \displaystyle \int f(x)\,dx in the form\displaystyle \int f(x)\,dx = \dfrac{1}{A}\ln|x+1|+\dfrac{1}{B}\ln|x-1| + \dfrac{D}{2x-2}+ C.where A,\,B and D are integer values, and C is a constant of integration.Fill in the correct values for A,\,B, and D.A = Answer 1 Question 23[input] B = Answer 2 Question 23[input] D = Answer 3 Question 23[input]

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