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Mathematical Applications for the Management, Life, and Social Sciences11th Edition

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Chapter 13.1, Problem 7E
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Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

Solutions

Chapter
Section
Problem 1CP
Problem 2CP
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
BuyFindarrow_forward

Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

In Problems 5-8, approximate the area under each curve by evaluating the function at the left-hand endpoints of the subintervals.

f ( x ) = 9 − x 2  from  x = 1  to  x = 1 ; 4  subintervals

To determine

To calculate: The area under the graph of f(x)=9−x2 from x=1 to x=3 using the 4 equal-intervals of the same size and use rectangles to find the exact area.

Explanation

Given Information:

The curve is f(x)=9−x2 from x=1 to x=3 and 4 subintervals and the function is evaluated at left end points of the subintervals.

Formula used:

The base of the rectangles to approximate the area is b−an where the interval [a,b] on which function is defined is divided into n subintervals.

The height of the rectangles is the value of the function calculated at the left-hand end point of the interval containing the base.

The area of a rectangle is baseĂ—height.

The approximated area under the curve is the sum of the areas of each rectangle.

The value of the sum ∑k=1nk3=(n(n+1)2)2.

Calculation:

Consider the curve f(x)=9−x2 from x=1 to x=3 and 4 subintervals where the function is evaluated at left end points of the subintervals.

The base of the rectangles to approximate the area is b−an where the interval [a,b] on which function is defined is divided into n subintervals.

Since, the function is defined from x=1 to x=3. So, a=1 and b=3.

Thus,

Base of each rectangle=3−14=0.5

Thus, the 4 subintervals, each of length 0.5 are [1,1.5], [1.5,2], [2,2.5] and [2.5,3].

Since, there are 4 subintervals, the number of rectangles is 4.

Recall that the height of the rectangles is the value of the function calculated at the left end point of the interval containing the base.

Record these values in a table.

Rectangle Base Left endpoint Height Area =baseĂ—height
1 0

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