Definite IntegrationHard

Question

The area bounded by the curve y = f(x), x-axis and the ordinates x = 1 and x = b is (b - 1) sin (3b + 4), ∀ b ∈ R, then f(x) =

Options

A.(x - 1) cos (3x + 4)
B.sin (3x + 4)
C.sin (3x + 4) + 3(x - 1) cos (3x + 4)
D.none of these

Solution

       
Required area (b - 1) sin (3b + 4) =
diff. w.r.t. b
3(b - 1) cos(3b + 4) + sin(3b + 4) = f(b)
⇒  f(x) = 3(x - 1) cos (3x + 4) + sin (3x + 4)

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