Explanation Given: Three constants a , b , c and three functions f ( x ) , g ( x ) , and h ( x ) . Concept used: Linear property of integral are as follows: ∫ [ a f ( x ) ± b g ( x ) ] d x = a ∫ f ( x ) d x ± b ∫ g ( x ) d x Proof: Consider the left-hand side of the given integral. ∫ [ a f ( x ) + b g ( x ) + c h ( x ) ] d x Now, apply linearity rule of sum as shown. ∫ [ a f ( x ) + b g ( x ) + c h ( x ) ] d x = ∫ [ a f ( x ) + b g ( x ) ] d x + ∫ c h ( x ) d x = ∫ a f ( x ) d x + ∫ b g ( x ) d x + ∫ c h ( x ) d x

6th Edition

ISBN: 9781465208880

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

Publisher: Kendall Hunt Publishing

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In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied unde…

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Question

Chapter 5.1, Problem 59PS

To determine

To show:That ∫[af(x)+bg(x)+ch(x)]dx=a∫f(x)dx+b∫g(x)dx+c∫h(x)dx .

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Chapter 5.1, Problem 58PS

Chapter 5.1, Problem 60PS

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For the given function, find (a) the equation of the secant line through the points where x has the given values and (b) the equation of the tangent line when x has the first value. y= f(x) = x²+x; x=-1,x=2 a. Which of the following formulas can be used to find the slope of the secant line? ○ A. 2-(-1) f(2) f(-1) 2+(-1) C. 1(2)+(-1) The equation of the secant line is 1(2)+(-1) О в. 2+(-1) f(2)-(-1) D. 2-(-1)

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Chapter 5 Solutions

Calculus

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That ∫ [ a f ( x ) + b g ( x ) + c h ( x ) ] d x = a ∫ f ( x ) d x + b ∫ g ( x ) d x + c ∫ h ( x ) d x .

Solution Summary: The author illustrates the linearity rule of sum of three constants a, b, and c.

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To show:That ∫[af(x)+bg(x)+ch(x)]dx=a∫f(x)dx+b∫g(x)dx+c∫h(x)dx .

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Chapter 5 Solutions