If I = ∫ x 5 + 1 x + 1 d x = f x + c and f 0 = 0 (where, c is the constant of integration), then

Question

If I = ∫ x 5 + 1 x + 1 d x = f x + c and f 0 = 0 (where, c is the constant of integration), then, f 1 > 1, 0 f 1 1, f 1 = 1, f 1 > 2

MARKS App · Accepted Answer

The given integral is I = ∫ x + 1 x 4 - x 3 + x 2 - x + 1 x + 1 d x = ∫ x 4 - x 3 + x 2 - x + 1 d x = x 5 5 - x 4 4 + x 3 3 - x 2 2 + x + c ∴ f x = x 5 5 - x 4 4 + x 3 3 - x 2 2 + x ∴ f 1 = 1 5 - 1 4 + 1 3 - 1 2 + 1 = 1 - 1 20 - 1 6 = 47 60 ⇒ 0 f 1 1

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