Explanation Given: The given function is: y = e − t 2 + 1 t + 1 and, n = 8 Approach: Trapezoidal Rule: Let f be a continuous function on [ a , b ] and let [ a , b ] be divided into n equal subintervals by the points a = x 0 , x 1 , x 2 , ⋯ , x n = b . Then, by the trapezoidal rule, ∫ a b f ( x ) d x ≈ ( b − a n ) [ 1 2 f ( x 0 ) + f ( x 1 ) + ⋯ + f ( x n − 1 ) + 1 2 f ( x n ) ] . Calculation: Consider the given function, y = e − t 2 + 1 t + 1 Take the integration: ∫ 1 9 ( e − t 2 + 1 t + 1 ) d t Here, n = 8 , b = 9 , a = 1 , f ( t ) = e − t 2 + 1 t + 1 and, b − a n = 9 − 1 8 = 1 Then, x i + 1 cab be calculated by x i + 1 = x i + b − a n . The corresponding function values will be calculated as below: i x i f ( x i ) 0 To determine (b) To find: The total reaction to the drug from t = 1 to t = 9 by using the Simpson’s Rule.

2nd Edition

ISBN: 9780321964038

Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher: Pearson Addison Wesley,

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Chapter 8.1, Problem 23E

To determine

(a)

To find:

The total reaction to the drug from t=1 to t=9 by using the trapezoidal rule.

To determine

(b)

To find:

The total reaction to the drug from t=1 to t=9 by using the Simpson’s Rule.

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Chapter 8.1, Problem 22E

Chapter 8.1, Problem 24E

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(a) To find: The total reaction to the drug from t = 1 to t = 9 by using the trapezoidal rule.

Solution Summary: The author explains how to find the total reaction to a drug by using the trapezoidal rule.

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(a)

To find:

The total reaction to the drug from t=1 to t=9 by using the trapezoidal rule.

(b)

To find:

The total reaction to the drug from t=1 to t=9 by using the Simpson’s Rule.

Want to see the full answer?

Chapter 8 Solutions

(a) To find: The total reaction to the drug from t = 1 to t = 9 by using the trapezoidal rule.

Solution Summary: The author explains how to find the total reaction to a drug by using the trapezoidal rule.

Concept explainers

Videos

(a) To find: The total reaction to the drug from t=1 to t=9 by using the trapezoidal rule.

(b) To find: The total reaction to the drug from t=1 to t=9 by using the Simpson’s Rule.

Want to see the full answer?

Chapter 8 Solutions

(a)

To find:

The total reaction to the drug from t=1 to t=9 by using the trapezoidal rule.

(b)

To find:

The total reaction to the drug from t=1 to t=9 by using the Simpson’s Rule.