(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.)

Name: (a) Let I =edx. Show that I2 =-x²-e-y?dx dy.R²(b) Reinterpret this do
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Description: (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

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Answered: (a) Let I = dx. Show that I² = dx dy.…

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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(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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