- #1
johndoe
- 41
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Homework Statement
Find the length pf the curve over the given interval.
[tex] r=1+\sin\theta [/tex]
[tex] 0\preceq\theta\preceq\2\pi [/tex]
The Attempt at a Solution
Ok I set it up as:
[tex] 2\pi[/tex]
[tex]\int\sqrt((1+\sin\theta)^2+cos^2\theta) [/tex]
0
and by simplifying and integrating, I get
[tex]2\pi [/tex]
[tex] -2\sqrt2[\sqrt(1-\sin\theta)] [/tex]
0
[tex] -2\sqrt2[(1-0)-(1-0)] =0 [/tex]
and obviously it is wrong,
I check the solution it has the same everything but the range ,
it obviously broke down the whole length into 2 times 1 piece from [tex] \pi/2 to 3\pi/2 [/tex] and the answer is 8
My question is why I get zero within my range, and why broke it down into the range above?
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