`int_0^1f(x)dx=1,\ int_0^1xf(x)dx=a ,\ int_0^1x^2f(x)dx=a^2,\ t h e n\ int_0^1(a-x)^2f(x)dx` equals a. `4a^2` b. `0` c. `2a^2` d. none of these

Explanation

`int_{0}^{1}(a-x)^{2} f(x) d x `

`=a^{2} int_{0}^{1} f(x) d x+int_{0}^{1} x^{2} f(x) d x-2 a int_{0}^{1} x f(x) d x `

`=a^{2} times 1+a^{2}-2 a a ldots ldots ldots ldots . ldots text { (As per given values) } `

`=2 a^{2}-2 a^{2} `

`=0`