exact for all polynomials of degree 2 or lessSolutionConside

exact for all polynomials of degree 2 or less.

Consider f(x)= Ax^2 + Bx + C

f(x)
= (Ax^2 + Bx + C)
= Ax^3/3 + Bx^2/2 + Cx

putting the limits (2,0) we have

= A(8/3) + 2B + 2c
= 8/3A + 2B + 2C ...(i)

Solving the RHS
Af(0) + Af(1) + Af(2)
=A(C) + A(A+ B+ C) + A(4A + 2B + C)

Rearranging terms we have,
=( A + 4A)A + ( A + 2A)B + ( A + A + A )C .....(ii)

Comparing coeffcient in equation (i) & (ii)

A + 4A= 8/3
A + 2A= 2
A + A + A=2

Solving these we get the values as
A =1/3, A=4/3, A =1/3