Learning objectives
Derive the arc length formula by approximating a curve with short straight segments and letting their length tend to zero, obtaining ∫√(1 + (dy/dx)²) dx
Calculate the length of a curve y = f(x) over a closed interval, setting up the integral exactly and evaluating it with technology when no elementary antiderivative exists
Explain why arc length measures total distance traveled along a curve rather than the straight-line displacement between its endpoints
Set up an arc length integral for a curve given with x as a function of y, integrating with respect to y over the appropriate interval
Check an arc length answer for reasonableness by comparing it with the straight-line distance between the endpoints, which it must exceed for any curve that is not a straight segment
Continue with a revision plan
These learning objectives are available to everyone. Sign in with an eligible plan to read the full note and worked examples.