Let f x be a continuous and positive function and the area bounded by y = f x , the x -axis and the lines x = 0 and x = a is 4 a 3 + sin ⁡ a sq. units a 0 . If f π 2 = k π 2 , then the value of k is

Question

Let f x be a continuous and positive function and the area bounded by y = f x , the x -axis and the lines x = 0 and x = a is 4 a 3 + sin ⁡ a sq. units a > 0 . If f π 2 = k π 2 , then the value of k is,

MARKS App · Accepted Answer

Given area is ∫ 0 a f x d x ∴ ∫ 0 a f x d x = 4 a 3 + sin ⁡ a Differentiating w.r.t. a , we get f a = 12 a 2 + cos ⁡ a ⇒ f π 2 = 3 π 2 ⇒ k = 3

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