• # question_answer The area bounded by the curve $y=f(x)$, x-axis and ordinates x = 1 and $x=b$is $\frac{5}{24}\pi$, then $f(x)$ is                    [RPET 2000] A)            $3(x-1)\cos (3x+4)+\sin (3x+4)$ B)            $(b-1)\sin (3x+4)+3\cos (3x+4)$ C)            $(b-1)\cos (3x+4)+3\sin (3x+4)$ D)            None of these

Area bounded by the curve $y=f(x),\,$x-axis and the ordinates $x=1$ and $x=b$ is $\int_{1}^{b}{f(x)\,dx}$                    \ From the question $\int_{1}^{b}{f(x)\,dx=(b-1)\sin (3b+4)}$                    Differentiate with respect to b, we get            $f(b)\,.\,1=3(b-1)\cos (3b+4)+\sin (3b+4)$                    $f(x)=3(x-1)\cos (3x+4)+\sin (3x+4)$.