Which of the following improper integrals is convergent?

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

Problem

Which of the following improper integrals is convergent? (a) ∫1∞1x dx\displaystyle \int_{1}^{\infty} \frac{1}{x}\,dx (b) ∫1∞1x ln⁡x dx\displaystyle \int_{1}^{\infty} \frac{1}{x\,\ln x}\,dx (c) ∫1∞1x1.1 dx\displaystyle \int_{1}^{\infty} \frac{1}{x^{1.1}}\,dx (d) ∫1∞1x0.8 dx\displaystyle \int_{1}^{\infty} \frac{1}{x^{0.8}}\,dx

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