题目
题目

ENG1090 - MUM S1 2025 Mock Final Exam

单项选择题

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

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标准答案
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思路分析
The problem asks us to evaluate the definite integral from 0 to 2 of (x+5)/(x^2-2x-3) with respect to x. First, notice the denominator factors as x^2-2x-3 = (x-3)(x+1). To integrate, decompose the fraction: (x+5)/((x-3)(x+1)) = A/(x-3) + B/(x+......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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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]

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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