Question

. If ${\int }_{sinx}^1{t}^2\left(f\right(t\left)\right)$ dt $=(1-\sin x)$, then $f\left(\frac{1}{\sqrt{3}}\right)$ is

• A. 1/3
• B. $1/\sqrt{3}$
• C. 3
• D. $\sqrt{3}$

Answer 1

Answer: (C)

3

${\int }_{sinx}^1{t}^2\left(f\right(t\left)\right)$ dt $=(1-\sin x)$
Differentiating both sides using Leibniz rule,
$\Rightarrow -{\sin }^{2}xf\left(\sin x\right).\cos x=-\cos x$
$\Rightarrow f\left(\sin x\right)=\frac{1}{{\sin }^{2}x}$
$\Rightarrow f\left(x\right)=\frac{1}{x^2}$

$\therefore f\left(\frac{1}{\sqrt{3}}\right)=3$