Quiz about Integration By Partial Fractions 2

Question 1

If the degree of numerator N(x) is equal or greater than the degree of denominator D(x), then the fraction is:

Accepted Answer

<p>improper</p>

Answer

<p>proper</p>

Question 2

$$\frac{2}{\left(x-2\right)\left(x+3\right)}$$ can be broken down into

Accepted Answer

$$\frac{A}{x-2}+\frac{B}{x+3}$$

Answer

$$\frac{A}{\left(x-2\right)^2}+\frac{B}{x+3}$$

Answer

$$\frac{A}{x-2}$$

Answer

$$\frac{B}{x+3}$$

Question 3

Which one should be used in the partial fraction decomposition of $$\frac{4x}{\left(x+1\right)\left(3+x^2\right)}?$$

Accepted Answer

$$\frac{A}{\left(x+1\right)}+\frac{Bx+C}{\left(3+x^2\right)}$$

Answer

$$\frac{A}{\left(x+1\right)}+\frac{B}{\left(3+x\right)}+\frac{C}{\left(3+x\right)^2}$$

Answer

$$\frac{A}{\left(x+1\right)}+\frac{B}{\left(3+x^2\right)}$$

Answer

$$\frac{A}{\left(3+x^2\right)}+\frac{Bx}{\left(1+x\right)}$$

Question 4

$$\frac{3x^2+x-1}{x^2-1}$$ is an improper fraction

Accepted Answer

True

Answer

False

Question 5

$$\frac{3x-1}{x^2-4}$$ cannot be broken down further.

Accepted Answer

False

Answer

True

Question 6

$$\frac{2x}{\left(3x^2+1\right)\left(3x+2\right)}$$ can be broken down into

Accepted Answer

$$\frac{Ax+B}{3x^2+1}+\frac{C}{3x+2}$$

Answer

$$\frac{1}{3}\left(\frac{Ax+B}{x^2+1}+\frac{C}{x+2}\right)$$

Answer

$$\frac{A}{3x^2+1}+\frac{B}{3x+2}$$

Answer

$$A+\frac{Bx+C}{3x^2+1}+\frac{D}{3x+2}$$

Question 7

I can use the following methods to find the unknown constant

Accepted Answer

All of the above

Answer

Substitution

Answer

Comparing coefficients

Answer

Cover up rule

Question 8

$$\int\frac{dx}{x^2+2x-15}$$

Accepted Answer

$$\frac{1}{4}\ln\left|x-3\right|-\frac{1}{8}\ln\left|x+5\right|+C$$

Answer

$$\frac{1}{8}\ln\left|x-3\right|-\frac{1}{8}\ln\left|x+5\right|+C$$

Answer

$$\frac{1}{8}\ln\left|x+5\right|-\frac{1}{8}\ln\left|x-3\right|+C$$

Answer

$$\frac{1}{4}\ln\left|x+5\right|-\frac{1}{4}\ln\left|x-3\right|+C$$

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