find the area of surface generated by revolving the are about y axis

Mar 2014
909
2
malaysia
the question is x = (e^t)(cos t ) , y = (e^t)(sin t ) , about y axis , where y = between 0 and 1
i have problem of finding the value of t when 1 = (e^t)(cos t ) and also 0 = (e^t)(cos t ) , since the integral cant be integrate so i let is as I .
how to continue form my working ? plo.jpg
 

HallsofIvy

MHF Helper
Apr 2005
20,249
7,909
?? You don't want to find t such that \(\displaystyle x= e^tcos(t)= 0\) and \(\displaystyle x= e^t cos(t)= 1\)! The problem specifically says that it is y that goes from 0 to 1. \(\displaystyle y= e^t sin(t)= 0\) for t= 0 and \(\displaystyle y= e^t sin(t)= 1\) when x is about -3.6.
 
Mar 2014
909
2
malaysia
?? You don't want to find t such that \(\displaystyle x= e^tcos(t)= 0\) and \(\displaystyle x= e^t cos(t)= 1\)! The problem specifically says that it is y that goes from 0 to 1. \(\displaystyle y= e^t sin(t)= 0\) for t= 0 and \(\displaystyle y= e^t sin(t)= 1\) when x is about -3.6.
other than that , is my other working correct ?
 
Mar 2014
909
2
malaysia
?? You don't want to find t such that \(\displaystyle x= e^tcos(t)= 0\) and \(\displaystyle x= e^t cos(t)= 1\)! The problem specifically says that it is y that goes from 0 to 1. \(\displaystyle y= e^t sin(t)= 0\) for t= 0 and \(\displaystyle y= e^t sin(t)= 1\) when x is about -3.6.
other than that , is my other working correct ?
 

Prove It

MHF Helper
Aug 2008
12,897
5,001
Work on your algebra...
 

Prove It

MHF Helper
Aug 2008
12,897
5,001
Look at your $\displaystyle \begin{align*} \left( \frac{\mathrm{d}x}{\mathrm{d}t} \right) ^2 \end{align*}$ term...
 
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Mar 2014
909
2
malaysia
Look at your $\displaystyle \begin{align*} \left( \frac{\mathrm{d}x}{\mathrm{d}t} \right) ^2 \end{align*}$ term...
can you point out the mistake directly ?
 
Mar 2014
909
2
malaysia
Look at your $\displaystyle \begin{align*} \left( \frac{\mathrm{d}x}{\mathrm{d}t} \right) ^2 \end{align*}$ term...
i have redo the question , but my ans is different from the ans given ... what is my mistake ?IMG_20151215_190121[1].jpgDSC_0340[1].JPG