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Question

The area enclosed by the curves y=sinx+cosx and y=|cosxsinx |over the interval [0,π2]is

A
4 (21)
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B
22(21)
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C
2 (2+1)
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D
22(2+1)
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Solution

The correct option is B 22(21)
cosx>sinx,xϵ(0,π4), and cosx<sinx,xϵ(π4,π2)
y1=sinx+cosx
y2=|cosxsinx|
Area
=π/20(y1y2)dx
= π/40 ((sinx+cosx)(cosxsinx))dx +π/2π/4((sinx+cosx)(sinxcosx))dx
=422

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