Question

Find the area bounded by the curve y = sin x between x = 0 and x = 2π.

Answer 1

Some points on the graph of y = sin x are as follows. The graph is obtained by joining these points with a curve.

x	0	${\displaystyle \frac{\pi }{6}}$	${\displaystyle \frac{\pi }{4}}$	${\displaystyle \frac{\pi }{3}}$	${\displaystyle \frac{\pi }{2}}$	${\displaystyle \frac{5\pi }{6}}$	${\displaystyle \frac{3\pi }{4}}$	${\displaystyle \frac{2\pi }{3}}$	${\displaystyle \pi }$
y	0	0.5	0.7	0.8	1	0.5	0.7	0.8	0

Area of ​​the required region

= Area of ​​the region bounded by the curve OPAQB and the x-axis

= Area of ​​sector OPA + Area of ​​sector AOB

= 2 Area of ​​sector OPA

${\displaystyle =2{\int }_0^{\pi }\sin x dx}$

${\displaystyle =2{[-\cos x]}_0^{\pi }}$

= 2[1 + 1]

= 2 × 2

= 4 square unit