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Chapter 4: Q. 7 (page 351)

If f(x)is defined atx=a, then鈭�aaf(x)dx=0. Explain why this makes sense in terms of area.

Short Answer

Expert verified

The width is zero so the area is zero.

Therefore the value is zero.

Step by step solution

01

Step 1. Given information

An expression is given as鈭�aaf(x)dx=0

02

Step 2. Drawing area

The integral is defined as

鈭�abf(x)dx=limn鈫�鈭�鈭�k=1nfxk*螖x

where 螖x=b-an,xk=a+k螖x&xk*=xk

So, the function fon the interval [a,a] and any nrectangles,

螖x=a-an=0

Since the width is zero therefore the area is zero,

鈭�aaf(x)dx=limn鈫�鈭�鈭�k=1nfxk*螖x=limn鈫�鈭�鈭�k=1nfxk*(0)=0

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