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Question

The value of π/2π/2dx[x]+[sinx]+4, where [t] denotes the greatest integer less than or equal to t, is : 


A
320(4π3)
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B
310(4π3)
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C
112(7π+5)
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D
112(7π5)
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Solution

The correct option is A 320(4π3)
I=π/2π/2dx[x]+[sinx]+4
  =1π/2dx21+4+01dx11+4+10dx0+0+4+π/21dx1+0+4
  =[x]1π/2+12[x]01+14[x]10+15[x]π/21
  =1+π2+12(0+1)+14(10)+15(π21)
  =920+3π5
  =320(4π3)

Mathematics

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