Explanation Given: The slope of a function F ( x ) is given as F ′ ( x ) = 2 x 1 − 3 x 2 . A point on the graph is given as ( 0 , 5 ) . Concept used: Slope of a function F ( x ) at point ( x 0 , y 0 ) is [ F ′ ( x ) ] ( x 0 , y 0 ) . Integration of a function can be defined by anti derivative of that function. For any function f ( x ) = a x + C , derivative of the function can be evaluated as f ′ ( x ) = a d d x ( x ) + d d x ( C ) = a ( 1 ) + 0 = a Therefore, antiderivative of a is given by ∫ a d x = a x + C Here, a is any constant and C is integrating constant. Formula used: Formula to evaluate the integral of the form ∫ a d x x is shown below. ∫ a d x x = a ∫ d x x = a ln | x | + C Formula to evaluate the integral of the form ∫ a x n d x is shown below. ∫ a x n d x = a ∫ x n d x = a x n + 1 n + 1 + C n ≠ − 1 Calculation: First, find out the function analytically. For analytic solution, let us find the antiderivative of the given slope

7th Edition

ISBN: 9781524916817

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

Publisher: Kendall Hunt Publishing

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Differential Equations

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Chapter 5.5, Problem 55PS

To determine

To find:The function F both graphically and analytically.

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Chapter 5.5, Problem 54PS

Chapter 5.5, Problem 56PS

Chapter 5 Solutions

Calculus

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The function F both graphically and analytically.

Solution Summary: The author explains how the function F is given graphically and analytically. Integration of a function can be defined by anti-derivative of that function.

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Chapter 5 Solutions