Explanation Given data: y The two curves / functions f ( x ) and g ( x ) continuous on interval [ a , b ] . Formula used: The definite integral of a continuous function f ( x ) ; A = ∫ a b f ( x ) d x estimates the area between the graph of the function f ( x ) and x -axis on an interval [ a , b ] Definition/ Explanation: The given functions f ( x ) and g ( x ) are continuous on interval [ a , b ] . Suppose the graphs of Functions f ( x ) and g ( x ) are as shown in figure here. The area between the curve f ( x ) and x -axis, i.e., area A B C E F A = ∫ a b f ( x ) d x The area between the curve g ( x ) and x -axis, i.e., area A D C E F A = ∫ a b g ( x ) d x Therefore, the area between the curves f ( x ) and g ( x ) on interval [ a , b ] is Area ABCDA = area ABCEFA - area ADCEFA A B C

5th Edition

ISBN: 9781429241861

Author: Laura Taalman, Peter Kohn

Publisher: W. H. Freeman

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Chapter 4, Problem 10D

To determine

To define:The area between two curves f(x) and g(x) on [a,b] .

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Chapter 4, Problem 9D

Chapter 4, Problem 11D

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2. [-/1 Points] DETAILS MY NOTES SESSCALCET2 5.5.003.MI. Evaluate the integral by making the given substitution. (Use C for the constant of integration.) x³ + 3 dx, u = x² + 3 Need Help? Read It Watch It Master It SUBMIT ANSWER 3. [-/1 Points] DETAILS MY NOTES SESSCALCET2 5.5.006.MI. Evaluate the integral by making the given substitution. (Use C for the constant of integration.) | +8 sec² (1/x³) dx, u = 1/x7 Need Help? Read It Master It SUBMIT ANSWER 4. [-/1 Points] DETAILS MY NOTES SESSCALCET2 5.5.007.MI. Evaluate the indefinite integral. (Use C for the constant of integration.) √x27 sin(x28) dx

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Chapter 4 Solutions

Calculus

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The area between two curves f ( x ) and g ( x ) on [ a , b ] .

Solution Summary: The author explains the definite integral of a continuous function f(x).

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Chapter 4 Solutions