Find the area of the surface generated bye + e -yeY + erevolving the curve x=- yin the interval2In 5Osys In 5 about the y-axis.

solution:-given curve x=ey+e-y2 in the interval 0≤y≤ln5revolving about the y-axisarea of a surface…

Answered: Find the area of the surface generated…

Find the area of the surface generated by eY + e -Y revolving the curve x = in the interval 2 In 5 Osys In 5 about the y-axis. 2.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter10: Analytic Geometry

Section10.6: The Three-dimensional Coordinate System

Problem 41E: Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?

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Question

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Find the area of the surface generated by
e + e -y
eY + e
revolving the curve x=
- y
in the interval
2
In 5
Osys In 5 about the y-axis.

Expert Solution

Step 1

$s o l u t i o n : - g i v e n c u r v e x = \frac{e^{y} + e^{- y}}{2} i n t h e i n t e r v a l 0 \leq y \leq \ln 5 r e v o l v i n g a b o u t t h e y - a x i s a r e a o f a s u r f a c e o f r e v o l u t i o n a b o u t y a x i s = \int_{a}^{b} 2 πx \sqrt{1 + {(\frac{dx}{dy})}^{2}} d y s u b s t i t u t i n g a = 0, b = \ln 5 \frac{dx}{dy} = \frac{d}{dy} (\frac{e^{y} + e^{- y}}{2}) = \frac{e^{y} - e^{- y}}{2}$

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