Area Question 26
Question 26
- The area bounded by the curves $y=f(x)$, the $X$-axis and the ordinates $x=1$ and $x=b$ is $(b-1) \sin (3 b+4)$. Then, $f(x)$ is equal to
$(1982,2 \mathrm{M})$
(a) $(x-1) \cos (3 x+4)$
(b) $8 \sin (3 x+4)$
(c) $\sin (3 x+4)+3(x-1) \cos (3 x+4)$
(d) None of the above
Show Answer
Solution:
- Since, $\int_{1}^{b} f(x) d x=(b-1) \sin (3 b+4)$
On differentiating both sides w.r.t. $b$, we get
$$ f(b)=3(b-1) \cdot \cos (3 b+4)+\sin (3 b+4) $$
$\therefore f(x)=\sin (3 x+4)+3(x-1) \cos (3 x+4)$
