   Chapter 7.8, Problem 4E

Chapter
Section
Textbook Problem

# (a) Graph the functions f ( x ) = 1 / x 1.1 and g ( x ) = 1 / x 0.9 in the viewing rectangles [0, 10] by [0, 1] and [0, 100] by [0, 1].(b) Find the areas under the graphs of ƒ and g from x = 1 to x = t and evaluate for t = 10 , 100 , 10 4 , 10 6 , 10 10 ,  and  10 20 .(c) Find the total area under each curve for x ≥ 1 , if it exists.

To determine

( a)

To graph:

The two given functions  f(x)=1x1.1 and g(x)=1x0.9

Explanation

Given:

f(x)=1x1.1 and g(x)=1x0.9

Formulae used:

The method of integral by direct integration

The curves in the rectangle [0,100] x [0, 1] is given below. Note that the green curve is f(x)=1x1.1 and orange curve is g(x)=1x0

To determine

(b)

To find:

The areas under the graph of f and g from x = 1 to x=t; and evaluate with various given values of t.

To determine

(c)

To find: The total area under the curve for x≥1 if it exists.

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