Is f(x)=1/root x an Integrable Function Whose Square is Not?

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SUMMARY

The function f(x) = 1/√x is integrable over the interval (0, 1) but its square, f(x)² = 1/x, is not integrable over the same interval. This conclusion is based on the properties of improper integrals, where the integral of f(x) from 0 to 1 converges, while the integral of f(x)² diverges. The discussion confirms that defining f(x) = 1/√x for 0 < x < 1 and f(x) = 0 otherwise is a valid approach to demonstrate this property.

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ss_1985
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Hi

The question asks to find out a function R--> R such that it is integrable, and its square is not.
Is f(x)=1/root x right?
The problem I thought was its only over an interval

Please help
thanks
 
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You can define the function as you stated for 0<x<1 and f(x)=0 otherwise.
 

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