Consider the graph of the parametric equations...

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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..

Guest May 8, 2021

CPhill · Answer 1 · 2021-05-08T05:28:56

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

CPhill · Answer 2 · 2021-05-08T05:42:39

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