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Chapter 4: Q. 78 (page 387)

Prove that for the region between the graph of a function f and the x-axis on an interval [a, b], the absolute area is always greater than or equal to the signed area.

Short Answer

Expert verified

Hence, proved.

Step by step solution

01

Step 1. Given Information.

The region is between the graph of a function f and the x-axis on an interval [a, b]

02

Step 2. Signed area and absolute area.

Signedarea:鈭�abf(x)dx.Absolutearea:鈭�abf(x)dx.

03

Step 3. Proof.

Asweallknow:x猢�x,So,fx猢�f(x),Therefore,weget,鈭�abf(x)dx猢�鈭�abf(x)dx.Hence,proved.

This proves that the absolute area is always greater than or equal to the signed area.

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