Which of the following definite integrals is improper for two distinct reasons and…

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

Problem

Which of the following definite integrals is improper for two distinct reasons and therefore must be rewritten as the sum of at least two separate integrals before evaluation? (a) ∫−∞∞e−x2 dx\displaystyle \int_{-\infty}^{\infty} e^{-x^{2}}\,dx (b) ∫0111−x dx\displaystyle \int_{0}^{1} \dfrac{1}{\sqrt{1-x}}\,dx (c) ∫−∞21(x−1)2 dx\displaystyle \int_{-\infty}^{2} \dfrac{1}{(x-1)^2}\,dx (d) ∫−221x2 dx\displaystyle \int_{-2}^{2} \dfrac{1}{x^{2}}\,dx

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