From calculus, the length of a curve is where f is a function whose graph is th...

From calculus, the length of a curve is

where f is a function whose graph is the curve on the interval a ? x ?b.

a. Find the length of the ellipse y² + 4x² = 1. Use the symmetry of the ellipse.

b. Verify the numerical approximation given for the arc length in the introductory example at the beginning of Chapter 3.