∫calculus i review

key term - Arc length

Definition

Arc length is the distance along a curve between two points. In calculus, it is calculated using integration techniques.

5 Must Know Facts For Your Next Test

  1. The formula for arc length in Cartesian coordinates is $\int_a^b \sqrt{1 + (f'(x))^2} \, dx$.
  2. For parametric equations, the arc length formula is $\int_a^b \sqrt{(\frac{dx}{dt})^2 + (\frac{dy}{dt})^2} \, dt$.
  3. When dealing with polar coordinates, the arc length can be computed as $\int_a^b \sqrt{r(\theta)^2 + (r'(\theta))^2} \, d\theta$.
  4. The arc length formula requires the derivative of the function representing the curve.
  5. Arc length calculations often involve definite integrals.

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