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For a bounded function, is the integral of the function from -infinity to +infinity defined and finite?

For a bounded function, is the integral of the function from -infinity to +infinity defined and finite? Correct Answer Not always

If the bounded function, is say y = 2, then the integral ceases to hold. Similarly, if it is just the block square function, it is finite. Hence, it depends upon the spread of the signal on either side. If the spread is finite, the integral will be finite.

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