94.9k views
0 votes
If the integral of the quantity 4 times x minus 2 and the product of the quantity x and the quantity x plus 1 dx = (A)Ln|x| + (B)Ln|x + 1| + constant, then what is the value of A - B? (5 points)

-8
-4
4
8

2 Answers

2 votes

Answer:

-8

Explanation:

f(x) = (4x − 2) / (x (x + 1))

Write f(x) as the sum of two fractions.

f(x) = A / x + B / (x + 1)

Combine back into one fraction using the least common denominator.

f(x) = (A (x + 1) + Bx) / (x (x + 1))

f(x) = ((A + B) x + A) / (x (x + 1))

This equals the original numerator of 4x − 2, so match the coefficients.

A + B = 4

A = -2

Solving for B, B = 6.

Therefore, A − B = -2 − 6 = -8.

User Jrotello
by
8.5k points
6 votes

Answer:

i think 8

Explanation:

User Roger Barreto
by
7.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories