∫f(x)dx, x∈[0, 1] = 1, ∫x f(x)dx, x∈[0, 1] = a and ∫x^2f(x)dx, x∈[0, 1] = a2 , then ∫(a - x)^2 f(x)dx, x∈[0, 1] is .......... .

Question

 \(\int\limits_{0}^{1}\)f(x)dx = 1, \(\int\limits_{0}^{1}\)x f(x)dx = a and \(\int\limits_{0}^{1}\)x²f(x)dx = a² , then \(\int\limits_{0}^{1}\)(a - x)² f(x)dx is .......... .

(a) 4 a²

(b) 0

(c) 2a²

(d) 1

Answer 1

(b) 0

 \(\int\limits_{0}^{1}\)(a - x)² f(x)dx = \(\int\limits_{0}^{1}\)(a² + x² -2ax) f(x)dx