How do you find the arc length of a polar curve?

Answer 1
We can find the arc length #L# of a polar curve #r=r(theta)# from #theta=a# to #theta=b# by
#L=int_a^bsqrt{r^2+({dr}/{d theta})^2}d theta#
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Answer 2

To find the arc length of a polar curve, you can use the formula:

[ L = \int_{\alpha}^{\beta} \sqrt{r(\theta)^2 + \left(\frac{dr}{d\theta}\right)^2} , d\theta ]

Where:

  • ( L ) is the arc length,
  • ( r(\theta) ) is the polar function,
  • ( \frac{dr}{d\theta} ) is the derivative of the polar function with respect to ( \theta ),
  • ( \alpha ) and ( \beta ) are the limits of integration.

You integrate this expression with respect to ( \theta ) over the given range of ( \theta ) values to find the total arc length of the curve.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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