Which statement best describes the improper integral ?

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

Problem

Which statement best describes the improper integral ∫−231x−1 dx\displaystyle \int_{-2}^{3} \frac{1}{x-1}\,dx? (a) It converges and its value is ln⁡(23)\ln\left(\dfrac23\right). (b) It diverges because the portions of area on either side of x=1x=1 grow without bound. (c) It converges and its value is ln⁡2\ln 2. (d) It diverges, but its Cauchy principal value exists and equals ln⁡(23)\ln\left(\dfrac23\right).

Related theory

Browse the problem library