Which of the following is an improper integral? A) the integral from 0 to 3 of the quotient of the quantity x plus 1 and the quantity 3 times x minus 2 dx
B) the integral from 1 to 3 of the quotient of the quantity x plus 1 and the quantity 3 times x minus 2 dx
C) the integral from negative 1 to 0 of the quotient of the quantity x plus 1 and the quantity 3 times x minus 2 dx
D) None of these

A)  

General Formulas and Concepts:

Calculus

Discontinuities

Integration

Step-by-step explanation:

Let's define our answer choices:

A)  

B)  

C)  

D) None of these

We can see that we would have a infinite discontinuity if x = 2/3, as it would make the denominator 0 and we cannot divide by 0. Therefore, any interval that includes the value 2/3 would have to be rewritten and evaluated as an improper integral.

Of all the answer choices, we can see that A's bounds of integration (interval) includes x = 2/3.

∴ our answer is A.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit:  Integration

Book: College Calculus 10e

the line of