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Integration with Partial Fractions

Authored by Charlotte Oliver-Bradley

Mathematics

12th Grade

CCSS covered

Used 2+ times

Integration with Partial Fractions
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10 questions

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1.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Find the partial fraction decomposition of the rational function: (3x + 2) / (x^2 + 5x + 6)

(1/(x + 2)) + (2/(x + 4))

(1/(x + 3)) + (2/(x + 4))

(1/(x + 2)) + (2/(x + 5))

(1/(x + 2)) + (2/(x + 3))

Tags

CCSS.HSA.APR.D.6

2.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Solve the following integral using partial fractions: ∫ (4x + 3) / (x^2 + 4x + 3) dx

ln|x + 1| + 3ln|x + 2| + C

ln|x + 2| + 3ln|x + 3| + C

ln|x + 1| + 3ln|x + 3| + D

ln|x + 1| + 3ln|x + 3| + C

3.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Express the rational function (2x^2 + 5x + 3) / (x^3 + 3x^2 + 2x) as a sum of partial fractions

(1/x) + (2/(x+1)) - (1/(x+2))

(1/x) + (2/(x+1)) + (1/(x+2))

(1/x) - (2/(x+1)) - (1/(x+2))

(1/x) - (2/(x+1)) + (1/(x+2))

Tags

CCSS.HSA.APR.D.6

4.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Evaluate the integral ∫ (x^2 + 3x + 2) / (x^3 + 4x^2 + 4x) dx using partial fractions

A ln|x| + B ln|x+2| + C/(x+2) + D

A ln|x| + B ln|x+2| - C/(x+2) + D

A ln|x| + B ln|x+2| - C/(x+2)

A ln|x| + B ln|x+2| + C/(x+2)

5.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Find the partial fraction decomposition of the rational function: (5x^2 + 7x + 2) / (x^2 + 6x + 8)

(1/(x + 4)) + (4/(x + 2))

(1/(x + 4)) + (4/(x + 2)) + (3/(x + 3))

(1/(x + 4)) + (4/(x + 2)) + (2/(x + 1))

(1/(x + 4)) + (4/(x + 2)) + (5/(x + 5))

Tags

CCSS.HSA.APR.D.6

6.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Solve the following integral using partial fractions: ∫ (3x + 1) / (x^2 + 2x + 1) dx

3ln|x + 1| + 2/(x + 1) + D

3ln|x + 1| + 2/(x - 1) + C

3ln|x + 1| + 2/(x + 1) + C

3ln|x + 1| + 2/(x - 1) + D

7.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Express the rational function (x^3 + 2x^2 + x) / (x^2 + 3x + 2) as a sum of partial fractions

(1/(x + 2)) + (1/(x + 3))

(1/(x + 1)) + (1/(x + 3))

(1/(x + 1)) + (1/(x + 2))

(1/(x + 1)) + (-1/(x + 2))

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

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