Let f (x) be a continuous function such that the area bounded by the curve $y = f (x)$, the x-axis, and the lines $x = 0$ and $x = a$ is $1+\frac{a^2}{2}\sin a$. Then,
Answer & explanation
Correct answer: option 3
It is given that $\int\limits_0^af(x)dx=1+\frac{a^2}{2}\sin a$
Differentiating this with respect to a, we get
$f(a)=a\sin a+\frac{1}{2}a^2\cos a$