part c (a) Let I =edx. Show that I2 =-x²-e-y?dx dy.R²(b) Reinterpret this double integral as a volume. Show that it's the volume of the shape we get when werevolve the space between eу-аxis.on top and 0 on bottom, 0 on the left and oo on the right, around the1(c) Use the shell method to calculate this volume in a different way. You should get that the volume equalsT. Use this to calculate I =- x2dx.(d) You can then use this to calculate (-)! =| t-1/2e-t dt. (Hint: Do a u-sub to get the integral to lookmore like I.)

Draw the curve y=e-x2, to identify the limits of integration from the region. Rotate the curve…

Answered: Use the shell method to calculate this…

Use the shell method to calculate this volume in a different way. You should get that the volume equals T. Use this to calculate I = dx.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

ChapterA: Appendix

SectionA.2: Geometric Constructions

Problem 10P: A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in...

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Question

part c

(a) Let I =
e
dx. Show that I2 =
-x²-
e
-y?
dx dy.
R²
(b) Reinterpret this double integral as a volume. Show that it's the volume of the shape we get when we
revolve the space between e
у-аxis.
on top and 0 on bottom, 0 on the left and oo on the right, around the
1
(c) Use the shell method to calculate this volume in a different way. You should get that the volume equals
T. Use this to calculate I =
- x2
dx.
(d) You can then use this to calculate (-)! =| t-1/2e-t dt. (Hint: Do a u-sub to get the integral to look
more like I.)

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