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Chapter 6: Q. 18 (page 539)

Suppose you wish to use n frustums to approximate the area of the surface obtained by revolving the graph of a function y = f (x) around the x-axis on [a, b]. Use a labeled graph to explain why the average radius r k of the kth frustum is given by,

rk=fxk-1+fxk2

Short Answer

Expert verified

Radius of frustum isrk=fxk-1+fxk2.

Step by step solution

01

Step 1. Given information .

Consider the given statement . Suppose you wish to use n frustums to approximate the area of the surface obtained by revolving the graph of a

function y = f (x) around the x-axis on [a, b].

02

Step 2. Classify the average radius of frustum .

Since f is continuous and the average lies between fxk-1and fxk, the Intermediate Value Theorem guarantees that there

is some point xkat whichfxkis equal tofxk-1+fxk2.

03

Step 3. Notation of the frustum .

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