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Circumference of an ellipse 
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#1
Feb1812, 12:05 AM

P: 33

all of my work so far is in the picture. i'm stuck on what i should do next.



#2
Feb1812, 05:06 AM

P: 615

your handwriting is incredibly neat, good show!



#3
Feb1812, 05:54 AM

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You are making the substitution [itex]x= a sin\theta[/itex] but then your integral has both x and [itex]\theta[/itex]. That's not right.
However, I would advise using the parametric equations [itex]x= a sin(\theta)[/itex], [itex]y= b cos(\theta)[/itex] rather than that complicated equation. 


#4
Feb1912, 04:48 PM

P: 33

Circumference of an ellipse



#5
Feb1912, 04:48 PM

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#6
Feb1912, 05:18 PM

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#7
Feb2112, 05:30 PM

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#8
Feb2112, 05:36 PM

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#9
Feb2112, 06:07 PM

P: 33

i completely reworked it, and it looks so much better now! lol.
now i have integral from 0 to a of sqrt(1 (b^2/a^2)cos(θ)) 


#10
Feb2112, 06:10 PM

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#11
Feb2112, 06:14 PM

P: 33

right. k = 1(b^2/a^2). did i cancel sin^2(θ) instead of cos(θ)?



#12
Feb2112, 06:23 PM

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#13
Feb2112, 07:00 PM

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sorry i'm a lot confused! 


#14
Feb2112, 09:37 PM

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#15
Feb2112, 10:24 PM

P: 33

but if k = 1  (b^2/a^2) and under the radical says 1ksin^2(θ), shouldn't the end result under the radical, when expanded, be 1  (sin(θ))^2 (b^2/a^2)(sin(θ))^2?
and where does the 4 outside the integral come from? 


#16
Feb2112, 10:29 PM

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