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Find The Region

  • Thread starter aks_sky
  • Start date
  • #1
55
0
Find the region enclosed by one leaf of the function r=2 sin2θ


Now i know how the diagram looks like for this function.
The diagram can be obtained by using :

x= r cosθ = 2 sin2θ cosθ
y= r sinθ = 2 sin2θ sinθ

Now i have to find the region enclosed by one of the leaves which i am not able to do.
I know i have to use the jacobian and also that i can use the above as cylindrical coordinates but what do i integrate? i dont know which function to integrate.

Any Suggestions for that??

thank you
 

Answers and Replies

  • #2
378
2
[tex]\frac{1}{2}\int r^{2} .d\theta[/tex]

You can use that formula
 
  • #3
berkeman
Mentor
56,634
6,532
[tex]\frac{1}{2}\int r^{2} .d\theta[/tex]

You can use that formula
Wouldn't it be [tex]\int r d\theta[/tex]

I could be missing something of course...
 
  • #4
55
0
Is the half for finding each half of the region of the leaf?
 

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