Area Bounded By Curve

Question

Let f(x)=x^−(1/2) and A denote the area of region bounded by f(x) and the x-axis, when x varies from -1 to 1.

A is nonzero and finite??

Answer 1

yes it is

Comments

Sayan Ghosh, Can you provide some explanation?

Are you getting the final area as 2(1-i) ? I calculated it by integrating in the range of -1 to 1. Is it the correct method?

---

Actually the answer is Area is non zero and finite because Area can never be zero but integration can be zero.(The difference as i have read in a prev gate question is that Area we take the positive summation only but for integration the summation can be -ve or +ve ( like in graph of x3 over -1 to 1 etc) ) .Hence, i said yes because he didn't ask for the actual sum.Coming to the actual sum, sqrt(x) is not defined from -1 to 0 hence unless we use complex values.But yes, if u use complex number then as you said the answer is coming 2(1-i).