Explanation Given: Any polynomial p ( x ) of degree less than or equal to 3. Formula used: Simpson’s rule to approximate integral is given by: ∫ a b f ( x ) d x ≈ Δ x 3 [ f ( x 0 ) + 4 ( f ( x 1 ) + f ( x 3 ) + ... + f ( x n − 1 ) ) + 2 ( f ( x 2 ) + f ( x 4 ) + ... + 2 f ( x n − 2 ) ) + f ( x n ) ] Where Δ x = b − a n Calculation: Consider the following figure for Any polynomial p ( x ) of degree less than or equal to 3. Here, S 1 and S 2 are parallel bases and h is height

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Concept explainers

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Question

Chapter 5.8, Problem 54PS

To determine

To show: for any polynomial p(x) of degree less than or equal to 3 ∫abp(x)dx=b−a6[p(a)+4p(a+b2)+p(b)]

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Chapter 5.8, Problem 53PS

Chapter 5.8, Problem 55PS

Chapter 5 Solutions

Calculus

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for any polynomial p ( x ) of degree less than or equal to 3 ∫ a b p ( x ) d x = b − a 6 [ p ( a ) + 4 p ( a + b 2 ) + p ( b ) ]

Solution Summary: The author explains the Simpson's rule for calculating volume within a prismoid.

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To show: for any polynomial p(x) of degree less than or equal to 3 ∫abp(x)dx=b−a6[p(a)+4p(a+b2)+p(b)]

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Chapter 5 Solutions