   Chapter 13, Problem 55RE ### 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

# Revenue A company has the data shown in the table from the sale of its product. x M R ¯ 0 0 2 480 4 720 6 720 8 480 10 0 If x represents hundreds of units and revenue R is in hundreds of dollars, approximate the total revenue from the sale of 1000 units by approximating ∫ 0 10 M R ¯ d x with the Trapezoidal Rule.

To determine

To calculate: The total revenue for the sale of 1000 units by the approximation of 010MR¯dx if the number of units in hundreds is x and revenue in hundreds of dollars is R. Use the Trapezoidal rule.

Explanation

Given information:

The provided integral is 010MR¯dx, where x is the number of units in hundreds and R is the revenue in hundreds of dollars. The table provided below shows the sale of its product.

xMR¯002480472067208480100

Formula used:

The Trapezoidal Rule for function f on the interval [a,b] is,

abf(x)dxh2[f(x0)+2f(x1)++2f(xn1)+f(xn)]

Where, h=ban and n is the number of equal subdivisions of [a,b].

Calculation:

Consider the integral, 010MR¯dx

Since, the lower limit is 0 and upper limit is 10. So, a=0 and b=10.

From the observation of the provided table, the number of subintervals is n=5.

Now, the value of h is,

h=ban

Substitute a=0, b=10 and n=5 in h=ban.

h=1005=2

The interval [0,10] is divided into 5 equal subintervals of width h=2

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