AP Calculus ABmediummcq1 pt

Which of the following is not integrable over the given closed interval?

A.021x1dx\int_0^2 \frac{1}{x-1}\,dx
B.02(x1)dx\int_0^2 (x-1)\,dx
C.02x1dx\int_0^2 |x-1|\,dx
D.02(x1)2dx\int_0^2 (x-1)^2\,dx

Explanation

Core Concept

The integrand 1x1\frac{1}{x-1} is unbounded at x=1x=1, which lies inside [0,2][0,2], so the integral does not exist.

Correct Answer

A021x1dx\int_0^2 \frac{1}{x-1}\,dx

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