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Question

The area bounded by y=x|sinx| and X-axis between x=0 and x=2π is

A
2π sq. units
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B
3π sq. units
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C
π sq. units
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D
4π sq. units
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Solution

The correct option is D 4π sq. units
y={xsinx,if xsinx0 i.e. 0xxxsinx>0, if xsinx<0 i.e.π<x2π
Therefore, required area =π0xsinxdx+2π0xsinxdx
=[x(cosx)]π0π0(cosx)dx[x(cosx)]2π0+π0(cosx)dx=4π sq. units
726459_681010_ans_3673f8464443468ebffc2224c9dc18aa.png

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