If for all real triplets a , b , c , f x = a + b x + c x 2 ; then ∫ 0 1 f x d x is equal to:

Question

If for all real triplets a , b , c , f x = a + b x + c x 2 ; then ∫ 0 1 f x d x is equal to:, 2 3 f 1 + 2 f 1 2, 1 2 f 1 + 3 f 1 2, 1 3 f 0 + f 1 2, 1 6 f 0 + f 1 + 4 f 1 2

MARKS App · Accepted Answer

∫ 0 1 a + b x + c x 2 d x = a x + b x 2 2 + c x 3 3 0 1 = a + b 2 + c 3 f 1 = a + b + c f 0 = a f 1 2 = a + b 2 + C 4 Now 1 6 f 1 + f 0 + 4 f 1 2 = 1 6 a + b + c + a + 4 a + b 2 + c 4 = 1 6 6 a + 3 b + 2 c = a + b 2 + c 3

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