Mathematics

Problem

Which of the following statements correctly describes the convergence and value of the integral

\displaystyle \int_{1}^{\infty} \frac{1}{x^{p}}\,dx

? a) It converges for

0<p<1

and equals

\dfrac{1}{1-p}

. b) It diverges for every real

p

. c) It converges for

p>1

and equals

\dfrac{1}{p-1}

. d) It converges for

p>1

and equals

\dfrac{p}{p-1}