Answer to Question #197216 in Real Analysis for Dharaba Parmar

Question #197216

Is f(x)=1/x^2/3in L₃[1 2] ?

Expert's answer

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^2/3in L₃[1 2]

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