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Chapter 5: Q. 3 (page 494)

What it means for a definite integral to be improper?

Short Answer

Expert verified

A definite integral is improper if at least one of the limit point is infinity or integrand function is discontinuous at least one point in range of the integral.

Step by step solution

01

Step 2. Definition

ADefinite integral 鈭�abfxdxis improper if

(i)At least on of the limit aorbare infinity or

(ii) role="math" localid="1651841753952" f(x)is discontinuous at least at one pointc鈭�a,b.

Point of discontinuous may or may not include the boundary point. And hence graph fxhas a vertical asymptote at that point.

02

Step 2. Example

鈭�蟺3蟺2sec2xdxis a definite which is improper because integrand fx=sec2xdiverge at x=蟺2and form vertical asymptote at x=蟺2.

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Most popular questions from this chapter

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