Explanation Given Information: The rocket is launched with the velocity 40 t 2 ft/sec and the subdivisions are n = 10 . Formula used: If a function f is continues then the left Riemann sum of the function f with n equal subdivisions over an interval [ a , b ] is, left riemann sum = ∑ k = 0 n − 1 f ( x k ) Δ x = f ( x 0 ) Δ x + f ( x 1 ) Δ x + .... + f ( x n − 1 ) Δ x = [ f ( x 0 ) + f ( x 1 ) + .... f ( x n − 1 ) ] Δ x Where the width of subdivision is Δ x = b − a n and the end points of the subdivisions are a = x 0 < x 1 < ⋅ ⋅ ⋅ ⋅ < x n = b . Calculation: Consider the rate of new member join Facebook, m ( t ) = 20 t 2 + 60 t + 12 Now draw the graph of m ( t ) = 20 t 2 + 60 t + 12 . Form the table for the value of the function at different points, t m ( t ) = 20 t 2 + 60 t + 12 0 12 1 92 2 212 3 372 Now plot the graph of the equation m ( t ) = 20 t 2 + 60 t + 12 as follows: Step1: Mark the points ( 0 , 12 ) ( 1 , 92 ) , ( 2 , 212 ) and ( 3 , 372 ) on the graph. Step2: Join the points The solution of the integral ∫ 1 6 m ( t ) d t is the area shaded in the graph, ∫ 1 6 ( 20 t 2 + 60 t + 12 ) d t Consider the subdivisions, n = 150 Compute the width of the subdivisions Δ t , Δ t = b − a n = 6 − 1 150 = 0

Finite Mathematics and Applied Calculus (MindTap Course List)

7th Edition

ISBN: 9781337274203

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 13.3, Problem 63E

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To calculate: The value of ∫16m(t)dt by using Riemann sum with 150 subdivisions and determine the significance of result, if the rate of new member join Facebook is m(t)=20t2+60t+12 million members per year 0≤t≤6 and t is the time in year from the start of 2007.

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Chapter 13.3, Problem 62E

Chapter 13.3, Problem 64E

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Chapter 13 Solutions

Finite Mathematics and Applied Calculus (MindTap Course List)

Ch. 13.1 - In Exercises 142, evaluate the integral. [HinT:...Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E Ch. 13.1 - Prob. 5E Ch. 13.1 - Prob. 6E Ch. 13.1 - Prob. 7E Ch. 13.1 - Prob. 8E Ch. 13.1 - Prob. 9E Ch. 13.1 - Prob. 10E

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The value of ∫ 1 6 m ( t ) d t by using Riemann sum with 150 subdivisions and determine the significance of result, if the rate of new member join Facebook is m ( t ) = 20 t 2 + 60 t + 12 million members per year 0 ≤ t ≤ 6 and t is the time in year from the start of 2007 .

Solution Summary: The author calculates the value of displaystyle 'underset' with Riemann sum with 150 subdivisions and determine the significance of the result.

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To calculate: The value of ∫16m(t)dt by using Riemann sum with 150 subdivisions and determine the significance of result, if the rate of new member join Facebook is m(t)=20t2+60t+12 million members per year 0≤t≤6 and t is the time in year from the start of 2007.

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Chapter 13 Solutions