Question

If $\int _ { \sin \mathrm { x } } ^ { 1 } \mathrm { t } ^ { 2 } \mathrm { f } ( \mathrm { t } ) \mathrm { dt }$ = (1 – sin x), then f $\left( \frac { 1 } { \sqrt { 3 } } \right)$ is equal to

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

Answer 1

Answer: (C)

3

Answer 2

Differentiating both sides with respect to x, we have

0 – sin²x f(sin x). cos x = – cos x

̃ f(sin x) =

[Q cos x ¹ 0 as t Î (sin x, sin p/2) so x¹ p/2]

̃ f(x) = 1/x²

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