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Consider the graph of the parametric equations


\(\begin{align*} x &= \frac{1}{\sqrt{t^2 + 1}},\\ y &= \frac{t}{\sqrt{t^2 + 1}}. \end{align*}\)

 

What is the area of the shape bounded by this graph and the y-axis? If this doesn't form a closed curve, answer with 0..

 May 8, 2021
 #1
avatar+120287 
+1

Note  that  x = 1  and  y  =  0   when  t  =  0....also...

 

Note  that   x  can never   =  0....so....this  curve  will never  intersect  the  y  axis.....

 

So......we  can  never  form a closed  curve

 

Area  = 0

 

 

cool cool cool

 May 8, 2021
 #2
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0

Thank you so much for looking at my problem, but I don't think your solution is correct. Would you mind taking another look at it if it's not too inconvenient?

Guest May 8, 2021
 #3
avatar+120287 
0

See  the  graph here  :  https://www.desmos.com/calculator/ehqpfxhrwz

 

Note  that no matter  what  t  is, we  can never  make  x  =  0  (we can get close, but  never 0 )

 

So.....this curve  never  intersects  the  y  axis   at all

 

So....no closed  curve  is  formed  by  this  curve  and the  y axis

 

cool cool cool

 May 8, 2021

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