Explanation Given: An integral is given as ∫ − 1 3 ( x 3 + 2 x 2 − 7 ) d x . Formula used: 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 ) ] Calculation: Consider the given integral. ∫ − 1 3 ( x 3 + 2 x 2 − 7 ) d x Here the function p ( x ) = x 3 + 2 x 2 − 7 is a polynomial of degree 3. Prismoidal rule can be used to evaluate the integral. a = − 1 , b = 3 The given integral can be evaluated as shown: ∫ − 1 3 ( x 3 + 2 x 2 − 7 ) d x = 3 − ( − 1 ) </

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

6th Edition

ISBN: 9781524908102

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 56PS

To determine

To calculate: The value of the integral ∫−13(x3+2x2−7)dx by Prismoidal rule.

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Chapter 5.8, Problem 55PS

Chapter 5.8, Problem 57PS

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Chapter 5 Solutions

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

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The value of the integral ∫ − 1 3 ( x 3 + 2 x 2 − 7 ) d x by Prismoidal rule.

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To calculate: The value of the integral ∫−13(x3+2x2−7)dx by Prismoidal rule.

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Chapter 5 Solutions