Question

The area bounded by $y=\frac{\sin x}{x},x-$axis and the ordinates $x=0,x=\frac{\pi }{4}$ is

• A. $=\frac{\pi }{4}$
• B. $<\frac{\pi }{4}$
• C. $>\frac{\pi }{4}$
• D. ${\int }_0^{\frac{\pi }{4}}\frac{\tan x}{x}dx$

Answer 1

Answer: (B)

$<\frac{\pi }{4}$

$\because x>0$
$\therefore \sin x<x$
$\Rightarrow \frac{\sin x}{x}<1$
or ${\int }_0^{\frac{\pi }{4}}\frac{\sin x}{x}<{\int }_0^{\frac{\pi }{4}}1.dx$
$=\frac{\pi }{4}$
or ${\int }_0^{\frac{\pi }{4}}\frac{\sin x}{x}<\frac{\pi }{4}$