Area under the curveMedium
Question
The area bounded by the curves y = f(x), the x-axis and the ordinates x = 1 and x = b is (b + 1) sin (3b + 4). Then, f(x) is
Options
A.(x -1) cos (3x + 4)
B.8 sin (3x + 4)
C.sin (3x + 4) + 3(x -1) cos(3x + 4)
D.None of the above
Solution
Since 
(b - 1)sin (3b + 4)
On differentiating both sides w. r. t. b, we get
f(b) = 3(b - 1). cos (3b + 4) + sin (3b + 4)
∴ f(x) = sin (3x + 4) + 3(x - 1) cos (3x + 4)
(b - 1)sin (3b + 4) On differentiating both sides w. r. t. b, we get
f(b) = 3(b - 1). cos (3b + 4) + sin (3b + 4)
∴ f(x) = sin (3x + 4) + 3(x - 1) cos (3x + 4)
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