[5 pts) Power series can also be used to approximate hard integrals. Consider the following integral that comes tip in a very important problem in classical mechanics: i a! 1 4 ds 4 [a vlosing () Here, 9 is an angle in radians [i.e., it is unitless). o is a snlall unitless constant [0 ii :1 cf, 1). d is a length in meters and y is the gravitational acceleration (in mfsg). This integral is actually impossible to solve in terms of elementary functions. But if a is small, we can approximate it. Do so by following these steps: (a) {1 pt) Using dimensional analysis, what are the units of the result of this integral? Show your steps. (b) {0 pts) Dene a: = rising I9. Now the integrand looks like i sol! where :1: is small because a is small. (e)I {1 pt) Approximate this function around a: = 0 using the the rst two terms of the binomial expansion (in I). (d) (1 pt) Now replace :1: with the original asin2 I? and perform the integral. Hint: You can use the trig identity sin2 3 = 1020523. The formula you get will be an approximation of the true integral, and will depend on the symbols {1, g, and o. (e)I {1 pt} Suppose d = 1m and o = 0.15. \"What is the Tvalue of your approximation? Include units! (f) (1 pt] Compare your approximation with the erect answer, which is given by dFa). Here, F is the socalled elliptic integral function\