Consider the integral I= _ - ^ 3 x-2 (x-1)^2 ,dx

MATHEMATICS · Multi-part · AP · Calculus BC · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Consider the integral I=∫−∞3x−2(x−1)2 dx.I=\int_{-\infty}^{3}\frac{x-2}{(x-1)^2}\,dx. The integrand is undefined at a finite point in the interval of integration and the interval itself is unbounded on the left. (a) Write II as the sum of two (or more, if necessary) definite integrals whose limits of integration create only proper integrals. Clearly indicate all limits that must be taken. (b) Evaluate each of the integrals obtained in part (a), showing the limit calculation required at each improper bound. (c) Determine whether II converges. Fully justify your conclusion by referencing the results from part (b).

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