Mathematics, 12.07.2021 15:40 jayc36809
Find the area of the surface generated by revolving the curve xequals=StartFraction e Superscript y Baseline plus e Superscript negative y Over 2 EndFraction ey+e−y 2 in the interval 0 less than or equals y less than or equals ln 20≤y≤ln2 about the y-axis.
Answers: 2
![$=\frac{\pi}{2} \left[ \frac{e^{2y}}{2} + \frac{e^{-2y}}{-2} + 2y \right]_2^{\ln 2}$](/tpl/images/1392/6741/13521.png)
![$=\frac{\pi}{2} \left[ \left(\frac{e^{2 \ln 2}}{2} + \frac{e^{-2\ln2}}{-2} + 2 \ln2 \right) - \left( \frac{e^0}{2} + \frac{e^0}{-2}+0\right) \right]$](/tpl/images/1392/6741/25529.png)
![$=\frac{\pi}{2}\left[ \frac{e^{\ln4}}{2} - \frac{e^{\ln(1/4)}}{2} + \ln 4 - \left( \frac{1}{2} - \frac{1}{2} + 0 \right) \right]$](/tpl/images/1392/6741/8f0b4.png)
![$=\frac{\pi}{2} \left[\frac{4}{2} -\frac{1/4}{2} + \ln 4 \right]$](/tpl/images/1392/6741/ce7f5.png)
![$=\frac{\pi}{2} \left[ 2-\frac{1}{8} + \ln 4 \right]$](/tpl/images/1392/6741/fbf87.png)
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Find the area of the surface generated by revolving the curve xequals=StartFraction e Superscript y...
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