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Question

The value of the integral, 31[x22x2]dx, where [x] denotes the greatest integer less than or equal to x, is

A
4
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B
5
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C
231
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D
23+1
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Solution

The correct option is C 231
I=31[x22x+13]dx
I=313dx+31[(x1)2]dx
Put x1=t dx=dt
I=(6)+20[t2]dt
I=6+100dt+211dt+322dt+233dt
I=6+(21)+2322+633
I=123

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