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Question

Area of the region bounded by the curve y = cos x between x = 0 and x = π is _______________.

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Solution

To find: area of the region bounded by the curve y = cosx between x = 0 and x = π



The required area of the region = 0πydx
Thus,
Required area=0πydx =0πcosxdx =0π2cosxdx+π2πcosxdx =sinx0π2+sinxπ2π =sinπ2-sin0+sinπ-sinπ2 =1-0+0-1 =1+-1 =1+1 =2Thus, Area=2 sq. units


Hence, the area of the region bounded by the curve y = cosx between x = 0 and x = π is 2 sq. units.

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