Question

The value of integral $\int _ { 1 / \pi } ^ { 2 / \pi } \frac { \sin ( 1 / x ) } { x ^ { 2 } } d x =$

• A. 2
• B. $- 1$
• C. 0
• D. 1

Answer 1

Answer: (D)

1

Answer 2

Put $t = \frac { 1 } { x } \Rightarrow d t = - \frac { 1 } { x ^ { 2 } } d x$as $t = \frac { \pi } { 2 }$and $\pi$

$= - \int _ { \pi / 2 } ^ { \pi } \sin t d t = - [ \cos t ] _ { \pi / 2 } ^ { \pi }$

$= - \left[ \cos \pi - \cos \left( \frac { \pi } { 2 } \right) \right] = 1$ .