For what values of does the improper integral _ 0 ^ 1 x^ p-1 x

MATHEMATICS · Subjective · AP · Calculus BC · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

For what values of

p>0

does the improper integral

\int_{0}^{1} x^{p-1} \ln x\, dx

converge? For those values of

p

, give the exact value of the integral in terms of

p