Question

If f(x) = a =+ bx + cx² where a, b, c ∈ R then ∫f(x)dx for x ∈ [0, 1] is

(1) 1/3(f(1) + f(0) + 2f(1/2))

(2) 1/6(f(1) + f(0) + 4f(1/2))

(3) 1/6(f(1) + f(0) - 4f(1/2))

(4) 1/6(f(1) - f(0) - 4f(1/2))

Answer 1

Answer is (2) 1/6(f(1) + f(0) + 4f(1/2))