0
$\begingroup$

How to manually sketch the graph of $\sqrt x+\sqrt y=1$ in order to find the area bounded by the curves $x+y=1$ and $\sqrt x+\sqrt y=1$ ?

The graph of the first function doesn't seem to any standard graph while the second one is the equation of a straight line . Any suggestions on how to roughly sketch it so that I can find the required area ?

  • 2
    You can always solve for $y$ here noting that $$ \sqrt{x} + \sqrt{y} = 1 \rightarrow y = 1 - 2 \sqrt{x} +x$$. This is a line that has been shifted by a $\sqrt{x}$ function and corresponds to a rotated parabola of sorts. Now sure how this is helpful to work with though. – 2017-02-26

2 Answers 2

0

You don't require to sketch the graph to find the area. Find where the teri graphs intersect. $√x+√y=1$ $x+y+2√xy=1$ But, $x+y=1$

So$√xy=0$

$x=0$. Or. $y=0$.

So when $x=0,y=1$ $y=0,x=1$

$(0,1). (1,0)$ are where they intersect.

Now you can use integration to find the area bounded by the curve and line between points $(1,0) ; (0,1)$ on X axis.

And the difference will give you the area between them.

  • 0
    Please format your answer to have some success on this site – 2017-02-26
  • 0
    @imranfat i am still learning the use of mathjax. – 2017-02-26
  • 0
    @ anonymous did you get it? – 2017-02-26
0

Take the graph of $x+y=1,$ which is a line thru $(0,1)$ and $(1,0).$ Take a few points $(x,y)$ on this line with $x\in [0,1/2].$ For each of them the points $(x^2,y^2)$ and $(y^2,x^2)$ will lie on the graph you wish to sketch. It won't take many points to get a good idea of the shape.