need to be done with C++ please.

Question written with red ink.

9 Question 9 submit code Complete elliptic integral of the second kind . There arc threc kinds of complete clliptic integrals (and thrcc incomplete elliptic intcgrals) . The complete elliptic integral of the second kind is given by the following integral 9.1 E(x)- dt For your information, for an ellipse with semi-major axis a and semi-minor axis b and eccen- tricity eell - V1 -b/a2, the circumference of the ellipse, say c, is given byc4aE(el) . The function E(x) can be expressed as power series as follows (9.2) . We shall compute the value of E() in two ways, by using the integral in eq. (9.1) and by . The integral in eq. (9.1) is im proper because the integrand diverges at t-1 (unless z = 1, 2.4/ 3 2.4-6 5 approximating the infinite series in eq. (9.2) by a finite sum. in which case we obtain 0/0, which a computer also cannot evaluate) 1. However, we can compute the integral in eq. (9.1) using the midpoint rule 2. Let I(x) denote the value of the integral in eq. (9.1) using the midpoint rule with n subintervals. . Let us approximate the infinite series in eq. (9.2) by a finite sum 1. Let S,(r) denote the value of the series in eq. (9.2), when the series is termi- nates at the term in 2m (z)-???1 (2)21 (2-3)23 (12-4-6 (2 2-1))22 %) 1-3-5...(2m-2m 2-4-6...(2n)2m -1 (9.3) 2. Formulate an efficient algorithm to compute the sum for Sm() in eq. (9.3) . (Optional/bonus) Prove using the sum in eq. (9.2) that E(x) is a decreasing func- tion ofx, i.e. ifx2 >:ri then E(?) :ri then E(?)