Assume that a 2 + (y/b)² = 1 shown in Figure 4. There is no explicit formula for L, but it is known that L = 4bG(k), with G(k) as in Exercise 96 and k = √1 − a²/b². Use the first three terms of the expansion of Exercise 96 to estimate L when a = 4 and b = 5.

Data From Exercise 96

The function is called an elliptic integral of the second kind. Prove that for |k|

y b a