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Question

The area bounded by y=x2+2 and y=2|x|cosπx is

A
13 sq. units
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B
23 sq. units
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C
43 sq. units
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D
83 sq. units
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Solution

The correct option is D 83 sq. units

y=x2+2, y=2|x|cosπx
Finding the intersection point:
x2+2=2|x|cosπx
|x|2+1+12|x|=cosπx
(|x|1)2+1=cosπx
Range of (|x|1)2+1 is [1,)
Range of cosπx is [1,1]
The equality is true only when (|x|1)2+1=cosπx=1
x=±1

Area under curve =11[(x2+2)(2|x|cos πx)]dx
=210[(x2+2)2x+cosπx]dx
=2[x33+2xx2+1πsinπx]10
=2[13+21+0]
=83 sq. units

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