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Question

20([x]2[x2])dx is equal to


A

4+3+2

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B

4+32

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C

4+23+2

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D

None of these

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Solution

The correct option is A

4+3+2


20([x]2[x2])dx=10([x]2[x2])dx+21([x]2[x2])dx=10(00)dx+211.dx21[x2]dx
[ If x lies between 0 and 1, then x2 also lies between 0 and 1]
=0+1[21[x2]dx+32[x2]dx+23[x2]dx]=1[211.dx+322.dx+233.dx]=1(21)2(32)3(23)=4+3+2


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