Explanation Given Information: The rate of change in the number of subscriber is, d S d t = 1000 t 2 e − t Where, 0 ≤ t ≤ 6 . Formula used: Simpson’s Rule: If f is continuous on [ a , b ] and n is an even integer, then ∫ a b f ( x ) d x , n = ( b − a 3 n ) [ f ( x 0 ) + 4 f ( x 1 ) + 2 f ( x 2 ) + 4 f ( x 3 ) + … + 4 f ( x n − 1 ) + f ( x n ) ] Calculation: Consider the rate of change in the number of subscriber is, d S d t = 1000 t 2 e − t So, the definite integral is ∫ 0 6 1000 t 2 e − t d t . Here, a = 0 b = 6 When n = 12 , the width of each subinterval is, 6 − 0 12 = 1 2 And the end points of subintervals are, x 0 = 0 x 1 = 1 2 x 2 = 1 2 + 1 2 = 1 And, x 3 = 1 + 1 2 = 3 2 x 4 = 3 2 + 1 2 = 2 And, x 5 = 2 + 1 2 = 5 2 x 6 = 5 2 + 1 2 = 3 And, x 7 = 6 2 + 1 2 = 7 2 x 8 = 7 2 + 1 2 = 4 And, x 9 = 4 + 1 2 = 9 2 x 10 = 9 2 + 1 2 = 5 And, x 11 = 10 2 + 1 2 = 11 2 x 12 = 11 2 + 1 2 = 6 Now, use Simpson’s rule, ∫ 0 6 1000 t 2 e

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Chapter 6.3, Problem 47E

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To calculate: The total increase in the number of subscribers during the first 6 years by the Simpson’s Rule with n=12 if the rate of change in the number of subscriber is dSdt=1000t2e−t where 0≤t≤6.

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Chapter 6.3, Problem 46E

Chapter 6.3, Problem 48E

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The total increase in the number of subscribers during the first 6 years by the Simpson’s Rule with n = 12 if the rate of change in the number of subscriber is d S d t = 1000 t 2 e − t where 0 ≤ t ≤ 6 .

Solution Summary: The author calculates the total increase in the number of subscribers during the first 6 years by the Simpson's Rule with n=12.

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To calculate: The total increase in the number of subscribers during the first 6 years by the Simpson’s Rule with n=12 if the rate of change in the number of subscriber is dSdt=1000t2e−t where 0≤t≤6.

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