   Chapter 6.2, Problem 59E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Revenue The revenue (in dollars) for a new product is modeled by R = 10 , 000 [ 1 − 1 / ( 1 + 0.1 t 2 ) 1 / 2 ] , where t is the time in years. Estimate the total revenue of the product over its first 2 years on the market.

To determine

To calculate: The total revenue of product over first two years on the market, where the revenue of the product is modelled as R=10000[11(1+0.1t2)1/2].

Explanation

Given Information:

The revenue of the product is modelled as R=10000[11(1+0.1t2)1/2].

Formula used:

The formula for the integral 1u2±a2du is;

1u2±a2du=ln|u±u2±a2|+C

The General power of integration rule:

undu=un+1n+1+C

Here, n is the any number.

General power differentiation Rule:

ddx[un]=nun1dudx

Calculation:

Consider the provided expression;

R=10000[11(1+0.1t2)1/2]

Integrate the above function from lower limit as 0 and higher limit as 2 in order to find the total revenue of product over first two years on the market, which can be written as:

R=0210000[11(1+0.1t2)1/2]dt=1000002[11(1+0.1t2)1/2]dt=10000[02dt021(1+0.1t2)1/2dt]

Rewrite

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