Question

The greater of $\int _ { 0 } ^ { \pi / 2 } \frac { \sin x } { x } d x$ and $\frac { \pi } { 2 }$ is

• A. $\frac { \pi } { 2 }$
• B. $\int _ { 0 } ^ { \pi / 2 } \frac { \sin x } { x } d x$
• C. Nothing can be said
• D. None of these

Answer 1

Answer: (A)

$\frac { \pi } { 2 }$

Answer 2

Since $\sin x < x$ for $0 < x \leq \pi / 2$

So, $\int _ { 0 } ^ { \pi / 2 } \frac { \sin x } { x } d x < \int _ { 0 } ^ { \pi / 2 } 1 d x = \frac { \pi } { 2 }$ .