Answer to Question #197216 in Real Analysis for Dharaba Parmar

Question

Is f(x)=1/x^2/3 in L₃[1 2] ?

Answer 1

for L₃[1 2] :

$\int^2_1|f(x)|^3dx<\infin$

then we have:

$\int^2_1x^{-2}dx=-1/x|^2_1=-1/2+1=1/2<\infin$

so,  f(x)=1/x^2/3 in L₃[1 2]