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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