Questions
ENG1090 - MUM S1 2025 Mock Final Exam
Single choice
Calculate the integral $$\int_0^2 \dfrac{x+5}{x^2-2x-3}\, dx$$
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Step-by-Step Analysis
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 explanationLog in for full answers
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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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