   Chapter 13.1, Problem 3E ### Mathematical Applications for the ...

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

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

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

# In Problems 1-4, approximate the area under each curve over the specified interval by using the indicated number of subintervals (or rectangles) and evaluating the function at the right-hand endpoints of the subintervals. (See Example 1.) f ( x )   =   9   − x 2  from  x =   1  to  x =   3 ;   4 subintervals

To determine

To calculate: The area under the curve f(x)=9x2 from x=1 to x=3 and 4 subintervals where the function is evaluated at right end points of the subintervals.

Explanation

Given Information:

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

Formula used:

The base of the rectangles to approximate the area is ban where the function is defined on [a,b].

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

The area A of a rectangle is Area=base×height.

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

Calculation:

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

The base of the rectangles to approximate the area is ban where the function is defined on [a,b].

Since, curve is defined from x=1 to x=3.

Thus,

base=314=0.5

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

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

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

Record these values in a table.

 Rectangle Base Right endpoint Height Area=base×height 1 0

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