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). Then, f (x) is __________ .

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sin (3x + 4) + 3 (x − 1) cos (3x +4) y = f\left( x ight) If A is the the area bound by the curve , x - axis , x = 1 and x = b \Rightarrow \int_1^b f\left( x ight) dx = \left[ A ight]_1^b = \left( b - 1 ight)\sin \left( 3b + 4 ight) .............\left\{	ext{Given }ight\} \Rightarrow f\left( x ight) = d/dx\left( \left( x - 1 ight)\sin\left( 3x + 4 ight) ight) = \sin\left( 3x + 4 ight)d/dx\left( x - 1 ight) + \left( x - 1 ight)d/dx\sin\left( 3x + 4 ight) = \sin\left( 3x + 4 ight) + 3\left( x - 1 ight)\cos\left( 3x + 4 ight)

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