Suppose we define the definite integral using the following formula `int_a^b f(x)dx=(b-a)/2
Channel: Doubtnut
Date: 2020-04-12

Suppose we define the definite integral using the following formula `int_a^b f(x)dx=(b-a)/2 (f(a)+f(b))`, for more accurate result for `c in (a,b), F(c)=(c-a)/2 (f(a)+f(c))+(b-c)/2(f(b)+f(c))` and when `c=(a+b)/2, int_a^b f(x)dx=(b-a)/4(f(a)+f(b)+2f(c))`In the above comprehension, if `f(x)` is a polynomial and `lim_(trarra) (int_a^t f(x)dx-(t-a)/2 [f(t)+f(a)])/(t-a)^3=0` for all `a` then the degree of `f(x)` can at most be (A) `1` (B) `2` (C) `3` (D) `4`