If In = (-x^n-1(a^2 - x^2)^3/2)/(n + 2) + kln - 2, then the value of k is

Question

Let n be a positive integer such that I_n = ∫xⁿ√(a² - x²)dx.  Then answer the following questions:

If I_n = (-x^n-1(a² - x²)^3/2)/(n + 2) + kl_{n - 2},  then the value of k is

(A) (n - 1)/(n + 2)

(B) (n + 2)/(n - 1)

(C) ((n - 1)/(n + 2))a²

(D) ((n + 2)/(n - 1))a² 

Answer 1

Answer is (C) ((n - 1)/(n + 2))a²