Let k be a fixed number with k > 1.

(a) Write a definite integral for the arc length L of the graph of y = x^ k from x = 0 to x = b. Do not try to solve the integral.
L=

b) One case when this integral can be evaluated exactly is when k = 3/2. In that case, use a substitution to evaluate the integral and find a formula for the arc length L in terms of b.
L = ?

(c) Another case when this integral can be evaluated exactly is when k = 2. In that case, use an inverse trig substitution to evaluate the integral and find a formula for the arc length Lin terms of b.
L = ?

(d) Use Simpson's Rule with n = 6 subintervals to estimate the arc length L of the curve when k = 3 and b = 1. Give your answer in decimal form with at least four decimal digits.
L = ?