   Chapter 12.2, Problem 45E ### 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 Suppose that the marginal revenue for a product is given by M R ¯ = − 30 ( 2 x + 1 ) 2 + 30 where x is the number of units and revenue is in dollars. Find the total revenue.

To determine

To calculate: The total revenue function if the marginal revenue for a commodity is MR¯=30(2x+1)2+30.

Explanation

Given Information:

The marginal revenue for a commodity is,

MR¯=30(2x+1)2+30.

Where x is the number of units.

Formula used:

According to the power rule of integrals,

xndx=xn+1n+1+C

Where x is variable and C is constant.

Calculation:

As it is provided that the marginal revenue for a commodity is,

MR¯=30(2x+1)2+30.

Now, the marginal revenue can be written as,

MR¯=30(2x+1)2+30=30(2x+1)2+30

Thus, the total revenue can be obtained by integrating the above function as,

R(x)=(30(2x+1)2+30)dx

Now, integrate the above function by the use of power rule of integrals as,

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