Question

Arc Length of a Polar Curve. Please see equation below.

Answer 1

\[L=\int\limits_{\alpha}^{\beta}\sqrt{r ^{2}+(dr/d \theta) ^{2}} d \theta \]

Problem: \[r=a\]

Answer 2

I know you can just use geometry to figure it out, but I'm required to use The arc length equation above.

Answer 3

I'm a little confused on the whole "r=a" portion. How am I to take to derivative of that?

Answer 4

I think that means you have \[a^2\]

Answer 5

Wouldn't that be for \[r ^{2} \]?
Is that also for \[dr/d\] ?

Answer 6

*dr/d(theta)

Answer 7

r=a means nothing by itself
assuming there is no drawing, I can only guess that this means that r is a constant, and the derivative of a constant is...?

Answer 8

zero

Answer 9

and then the integral becomes trivial, yes
if there is another interpretation to the problem I think more info is required. what the heck is "a" ?

Answer 10

There is no drawing. The problem from the text is "The entire circle r=a" That's all that's given. :/

Answer 11

Then I interpret the problem as I stated above. If you don't disagree with me I think you should try to take it from there.

Answer 12

I still don't get it... I understand you take the integral but overall I'm just confused