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**1. 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]

**3. 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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