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Question

The area bounded by the curve y=cosx, the x-axis and the ordinates x=0and x=2π


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Solution

The area bounded by the curve y=cosx, the x-axis and the ordinates x=0and x=2π

is given by-

Area bounded =02πydx

=02πcosxdx=0π2cosxdx+π23π2cosxdx+3π22πcosxdx=sinx0π2-sinxπ23π2+sinx3π22π=sinπ2-sin0-sin3π2-sinπ2+sin2π-sin3π2=1-0--1-1+0+1=1+2+1=2+2=4squnits

Hence, the area bounded is4sq.units


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