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The value of k N for which the integral In = 01 (1 - xk )n dx, n N, satisfies 147 I20 = 148 I21 is
(3) 7
By parts (taking 1 as the second function):
In = [x (1 - xk )n ]01 + nk 01 xk (1 - xk )n - 1dx
= nk 01 [ (1 - xk )n - 1 - (1 - xk )n ]dx ( xk = 1 - (1 - xk ) )
In = nk (In - 1 - In ) InIn - 1 = nknk + 1
n = 21: I21I20 = 21k21k + 1 = 147148
21k = 147 k = 7
Answer: (3)
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