Mathematics

Mathematics

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).

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