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

Intermediate Algebra
10th Edition
ISBN:9781285195728
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter7: Equations And Inequalities In Two Variables
Section7.1: Rectangular Coordinate System And Linear Equations
Problem 59PS: Now lets use a graphing calculator to get a graph of C=59(F32). By letting F=x and C=y, we obtain...
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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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