Consider the improper integral

MATHEMATICS · Single correct · AP · Calculus BC · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

\displaystyle\int_{0}^{3}\frac{1}{(x-1)^2}\,dx

. Which of the following is true? (a) The integral diverges because the integrand has a vertical asymptote at

x=1

, so no finite value exists. (b) The integral converges and equals

1

. (c) The integral diverges because the integrand is unbounded at

x=0

. (d) The integral converges and equals

\dfrac{3}{2}