Explanation Given : The line y = m x divides the curve y = x ( 1 − x ) over [ 0 , 1 ] . Formula Used : Integrating the given curve to determine area under the curve as A r e a = ∫ a b f ( x ) d x Calculation : Firstly finding the area under the given curve: ∫ 0 1 x ( 1 − x ) d x = ∫ 0 1 ( x − x 2 ) d x = [ 1 2 x 2 − 1 3 x 3 ] 0 1 = 1 6 Now, the line y = m x intersect the curve y = x ( 1 − x ) when, → m x = x ( 1 − x ) ⇒ x 2 − x ( 1 − m ) = 0 ⇒ x = 0 , 1 − m So the line intersect at two points x = 0 , x = 1 − m The area under the curve for the divided region:

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Question

Chapter 6.1, Problem 63E

To determine

The line $y = m x$ that divides the area under the curve $y = x (1 - x)$ for the interval $[0, 1]$ into two equal areas.

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Chapter 6 Solutions

Calculus - Standalone book

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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The line y = m x that divides the area under the curve y = x ( 1 − x ) for the interval [ 0 , 1 ] into two equal areas.

Solution Summary: The author explains how the line y = m x divides the area under the curve into two equal areas.

Concept explainers

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The line $y = m x$ that divides the area under the curve $y = x (1 - x)$ for the interval $[0, 1]$ into two equal areas.

Chapter 6 Solutions

The line y = m x that divides the area under the curve y = x ( 1 − x ) for the interval [ 0 , 1 ] into two equal areas.

Solution Summary: The author explains how the line y = m x divides the area under the curve into two equal areas.

Concept explainers

Videos

The line y=mx that divides the area under the curve y=x(1−x) for the interval [0,1] into two equal areas.

Chapter 6 Solutions

The line $y = m x$ that divides the area under the curve $y = x (1 - x)$ for the interval $[0, 1]$ into two equal areas.