Find the area bounded by the curve y=sin x between x=0 and x=2π
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
If 5f(x) + 4f (\(\frac{1}{x}\)) = \(\frac{1}{x}\)+ 3, then \(18\int_{1}^{2}\) f(x)dx is: