Find the area bounded by the curve y=sin x between x=0 and x=2π
Find the area bounded by the curve y=sin x between x=0 and x=2π
Solution and Explanation
The graph of y=sin x can be drawn as
∴Required area=Area OABO+Area BCDB
=
\[\int_{0}^{π} \sin x \,dx\]+
\[+\int_{π}^{2π} \sin x\,dx\]=[-cosx]π0+|[-cosx]2ππ|
=[-cosπ-cos0]+|-cos2π+cosπ|
=1+1+|(-1-1)|
=2+|-2|
=2+2=4units
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