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Using your previous work, find the region bounded by the curves y = x² and y = x³.

Using your previous work, find the region bounded by the curves y = x² and y = x³.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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3.2 is the previous work

a 3.2 3 yex bainded area by curves 2 2 2 3-4 2(2)
Transcribed Image Text:a 3.2 3 yex bainded area by curves 2 2 2 3-4 2(2)
Using your previous work, find the region bounded by the curves y = x² and y = x°. (Hint: consider the picture and relate it to 3.1 and 3.2) (Note: it is important that x° < x² < x on (0, 1) for this result to hold - without ordering and interval conditions like above, this trick will not work. For instance, consider the regions = x, y = -2x² + 1, and y = x°. The area between the first two curves is (as you can verify) and the area between the second two curve is about 1.0075, but we know - 1.0075 - 0.1175 for several bounded by Y 8 that the area between the first and third curves is not - reasons. One of the reasons is that we have found the area between the first and third curves to be different already; a second one is that the curves do not maintain an ordering on the intervals where the regions occur; a third reason is that the regions do not occur in the same intervals.)
Transcribed Image Text:Using your previous work, find the region bounded by the curves y = x² and y = x°. (Hint: consider the picture and relate it to 3.1 and 3.2) (Note: it is important that x° < x² < x on (0, 1) for this result to hold - without ordering and interval conditions like above, this trick will not work. For instance, consider the regions = x, y = -2x² + 1, and y = x°. The area between the first two curves is (as you can verify) and the area between the second two curve is about 1.0075, but we know - 1.0075 - 0.1175 for several bounded by Y 8 that the area between the first and third curves is not - reasons. One of the reasons is that we have found the area between the first and third curves to be different already; a second one is that the curves do not maintain an ordering on the intervals where the regions occur; a third reason is that the regions do not occur in the same intervals.)
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