If R=5050∫10(1−x50)100dx∫10(1−x50)101dx, then the value of R is
A
5051
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B
5052
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C
5053
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D
5054
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Solution
The correct option is A 5051 Dr=∫10(1−x50)101.1dxDr=[x(1−x50)101]10−∫10x(101)[1−x50]100(−50x49)dx=(5050)∫10(1−x50)100[x50−1+1]dx=Nr−(5050)Dr∴R=NrDr=NrNr−(5050)Dr=11−(5050)DrNr∴R=5050+1=5051