Explanation Given : The equation of a semicubical parabola y 2 = x 3 and line x = 1 . Formula used : Area bounded by a curve along x -axis is calculated using the formula as given below, A r e a = ∫ a b ( y = f ( x ) ) d x Area bounded by two curves along y -axis is calculated using the formula as given below, A r e a = ∫ a b ( C u r v e t o t h e r i g h t – C u r v e t o t h e l e f t ) d y Calculation : The given semicubical parabola y 2 = x 3 , and line x = 1 can be drawn as, and we are required to find the shaded area We will first calculate the area by integrating along x-axis and then along y-axis. Symbolically, writing the given equation as y = x 3 2 Therefore, A r e a = ∫ 0 1 ( x 3 2 ) d x Integrating above expression to get the area bounded, we get = ( 2 x 5 2 5 ) | 0 1 = ( 2 ( 1 ) 5 2 5 ) − ( 2 ( 0 ) 5 2 5 ) Evaluating the above limits, we get = ( 2 ( 1 ) 5 2 5 ) = ( 2 5 ) Therefore, the area bounded by the two curves is 2 5 sq. units. Now, we will find the area along y-axis...

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ISBN: 9781319055844

Author: FRANZOSA

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Chapter 6.1, Problem 28E

To determine

The area under the curve and a line.

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Chapter 6.1, Problem 27E

Chapter 6.1, Problem 29E

Chapter 6 Solutions

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Ch. 6.1 - Prob. 1PQ Ch. 6.1 - Prob. 2PQ Ch. 6.1 - Prob. 3PQ Ch. 6.1 - Prob. 4PQ Ch. 6.1 - Prob. 5PQ Ch. 6.1 - Prob. 6PQ Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E

Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E Ch. 6.1 - Prob. 7E Ch. 6.1 - Prob. 8E Ch. 6.1 - Prob. 9E Ch. 6.1 - Prob. 10E Ch. 6.1 - Prob. 11E Ch. 6.1 - Prob. 12E Ch. 6.1 - Prob. 13E Ch. 6.1 - Prob. 14E Ch. 6.1 - Prob. 15E Ch. 6.1 - Prob. 16E Ch. 6.1 - Prob. 17E Ch. 6.1 - Prob. 18E Ch. 6.1 - Prob. 19E Ch. 6.1 - Prob. 20E Ch. 6.1 - Prob. 21E Ch. 6.1 - Prob. 22E Ch. 6.1 - Prob. 23E Ch. 6.1 - Prob. 24E Ch. 6.1 - Prob. 25E Ch. 6.1 - Prob. 26E Ch. 6.1 - Prob. 27E Ch. 6.1 - Prob. 28E Ch. 6.1 - Prob. 29E Ch. 6.1 - Prob. 30E Ch. 6.1 - Prob. 31E Ch. 6.1 - Prob. 32E Ch. 6.1 - Prob. 33E Ch. 6.1 - Prob. 34E Ch. 6.1 - Prob. 35E Ch. 6.1 - Prob. 36E Ch. 6.1 - Prob. 37E Ch. 6.1 - Prob. 38E Ch. 6.1 - Prob. 39E Ch. 6.1 - Prob. 40E Ch. 6.1 - Prob. 41E Ch. 6.1 - Prob. 42E Ch. 6.1 - Prob. 43E Ch. 6.1 - Prob. 44E Ch. 6.1 - Prob. 45E Ch. 6.1 - Prob. 46E Ch. 6.1 - Prob. 47E Ch. 6.1 - Prob. 48E Ch. 6.1 - Prob. 49E Ch. 6.1 - Prob. 50E Ch. 6.1 - Prob. 51E Ch. 6.1 - Prob. 52E Ch. 6.1 - Prob. 53E Ch. 6.1 - Prob. 54E Ch. 6.1 - 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Prob. 39CRE Ch. 6 - Prob. 40CRE Ch. 6 - Prob. 41CRE Ch. 6 - Prob. 42CRE Ch. 6 - Prob. 43CRE Ch. 6 - Prob. 44CRE Ch. 6 - Prob. 45CRE Ch. 6 - Prob. 46CRE Ch. 6 - Prob. 47CRE Ch. 6 - Prob. 48CRE Ch. 6 - Prob. 49CRE Ch. 6 - Prob. 50CRE Ch. 6 - Prob. 51CRE Ch. 6 - Prob. 52CRE Ch. 6 - Prob. 53CRE Ch. 6 - Prob. 54CRE

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The area under the curve and a line.

Solution Summary: The author explains the equation of a semicubical parabola y 2 = x 3 and line X = 1 and calculates the area bounded by the two curves.

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The area under the curve and a line.

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Chapter 6 Solutions