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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.

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.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter8: Further Techniques And Applications Of Integration
Section8.3: Volume And Average Value
Problem 22E
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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.)
Transcribed Image Text:(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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