Determine the set of all real numbers for which the integral converges.

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

Problem

Determine the set of all real numbers

p

for which the integral

\displaystyle \int_{0}^{\infty} \frac{x^{p}}{1+x^{2}}\,dx

converges. (a)

p<-1

(b)

-1<p<1

(c)

p>-1

(d)

p<1