Question

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

(a) Yes

(b) Never

(c) Not always

(d) None of the mentioned

This question was posed to me in semester exam.

My doubt is from Signal Classification and Properties in chapter Signals and Systems Basics of Signals and Systems

Answer 1

Correct answer is (c) Not always

Explanation: 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.