   Chapter 13.1, Problem 1E ### 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 ) =   4 x −   x 2  from  x =   0  to  x =   2 ;   2 subintervals

To determine

To calculate: The area under the curve f(x)=4xx2 from x=0 to x=2 and 2 subintervals where the function is evaluated at right end points of the subintervals.

Explanation

Given Information:

The curve is f(x)=4xx2 from x=0 to x=2 and 2 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 [b,a].

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 A=base×height.

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

Calculation:

Consider the curve f(x)=4xx2 from x=0 to x=2 and 2 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=0 to x=2.

Thus,

base=202=1

Thus, the 2 subintervals, of length 1 are [0,1] and [1,2]

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