If ∫ 2 x 12 + 5 x 9 x 5 + x 3 + 1 3 d x = 1 2 f x + C , then f ( 1 ) - f ( 0 ) =

Question

If ∫ 2 x 12 + 5 x 9 x 5 + x 3 + 1 3 d x = 1 2 f x + C , then f ( 1 ) - f ( 0 ) =, 1 2, 1 9, 1 27, 1 54

MARKS App · Accepted Answer

I = ∫ 2 x 12 + 5 x 9 x 5 + x 3 + 1 3 d x = 1 2 f x + c ⇒ I = ∫ 2 x - 3 + 5 x - 6 1 + x - 2 + x - 5 3 d x Put 1 + x - 2 + x - 5 = t ⇒ - 2 x - 3 - 5 x - 6 d x = d t ⇒ I = - ∫ d t t 3 = 1 2 t 2 + C So, f x = 1 1 + x - 2 + x - 5 2 = x 10 x 5 + x 3 + 1 2 f 1 - f 0 = 1 9 - 0 = 1 9

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