Partial Fractions & Integration Quiz

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10-question calculus quick quiz.

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Yaj Kotak

United States

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Partial Fractions & Integration Quiz


Froggy Jumps Partial Fractions & Integration QuizOnline version 10-question calculus quick quiz. by Yaj Kotak 1 1. When decomposing a rational function using partial fractions, which condition must be met first? a C) The denominator must be irreducible b B) The degree of the numerator must be less than the degree of the denominator c A) The degree of the numerator must be greater than the degree of the denominator 2 2. If a rational function has a denominator of (x − 4)(x − 5), which form is appropriate for partial fraction decomposition? a A) A/(x − 4) + B/(x − 5) b D) A/(x − 9) c B) A/(x − 4)^2 + B/(x − 5)^2 3 3. In integration by parts, which choice of u is generally preferred? a A) The expression that simplifies when differentiated b B) The expression with the highest power c D) The expression inside the integral bounds 4 4. Which formula represents integration by parts? a B) ∫ u dv = uv − ∫ v du b C) Integral of a dx = ax + C c A) Integral of f(g(x))g'(x) dx 5 5. A u-substitution is most useful when an integral contains: a A) A rational function b C) A function and its derivative c D) A constant multiple only 6 6. When using u-substitution for a definite integral, what must be done after changing variables? a A) Ignore the bounds b D) Use integration by parts c B) Convert the bounds to u-values 7 7. If u = x^2 + 1, what is du in terms of x? a D) du = 2 dx b A) du = 2x dx c B) du = x dx 8 8. Why is polynomial long division sometimes required before partial fraction decomposition? a C) To make the rational function proper b A) To factor the denominator c B) To simplify constants 9 9. A definite integral represents: a B) The exact value of an antiderivative b A) The slope of a function c C) Net area under a curve on an interval 10 10. Which technique is most appropriate for evaluating the integral of x e^(x^2) dx? a B) Integration by parts b A) Partial fractions c C) U-substitution

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Partial Fractions & Integration Quiz

Froggy Jumps

About this activity

Created by

Download the paper version to play

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Partial Fractions & Integration QuizOnline version

by Yaj Kotak

1. When decomposing a rational function using partial fractions, which condition must be met first?

2. If a rational function has a denominator of (x − 4)(x − 5), which form is appropriate for partial fraction decomposition?

3. In integration by parts, which choice of u is generally preferred?

4. Which formula represents integration by parts?

5. A u-substitution is most useful when an integral contains:

6. When using u-substitution for a definite integral, what must be done after changing variables?

7. If u = x^2 + 1, what is du in terms of x?

8. Why is polynomial long division sometimes required before partial fraction decomposition?

9. A definite integral represents:

10. Which technique is most appropriate for evaluating the integral of x e^(x^2) dx?