I want to prove T(x)=(sin x)^(k) is Lebesgue integrable on [o,pi]
how can i define upper and lower bounde to show? and solove?
please tell for all value of k, is this Lebesgue integrable? for odd or even value of k, what is status?
"we want to to show that the reimann integral is correct using Lebesgue integral, so I need to show first T(x)= (sinx)^k, is limited for a lower and upper bounds. so I must to show the upper and lower bounds for T(s). then I will tell when n trend to inf, T(s) is integrable with Lebesgue
For all $k\geq 0$, $\ \sin^kx$ is continuous on $[0,\pi]$, so is Riemann (and hence Lebesgue) integrable.