Evaluate the integral below and sketch the graph of the family member that passes through the point (1, 2).
A)
B)
C)
D)
E)

Question

Evaluate the integral below and sketch the graph of the family member that passes through the point (1, 2). ​  ​
A) ​ ​ 
B) ​ ​ 
C) ​ ​ 
D) ​​ ​ 
E) ​​ ​

Quizplus · Accepted Answer

Integrating the given expression, we get:

$$\int\frac{1}{x-1} dx = \ln|x-1| + C$$

This represents a family of logarithmic curves. To find the value of the constant $C$, we use the given point (1,2):

$$\ln|1-1|+C = \ln|0|+C$$

This is undefined, so the curve cannot pass through the point (1,2).

Therefore, the correct answer is B, as none of the curves in the family pass through the given point.

Evaluate the Integral Below and Sketch the Graph of the Family