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Question

If I1=10(1x50)100dx and I2=10(1x50)101dx such that I2=αI1 then α equals to:

A
50505049
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B
50505051
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C
50515050
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D
50495050
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Solution

The correct option is B 50505051

I1=10(1x50)100dx
I2=10(1x50)(1x50)100dx
=10(1x50)100dx10x50(1x50)100dx
I2=I110xIx49(1x50)100IIdx
By using by parts
1x50=t
x49dx=dt50
I2=I1[x(150)(1x50)101101]10+01(150)(1x50)101101dx
I2=I10+10(1x50)101(5050)
I2=I1I25050
50515050I2=I1
I2=50505051I1
α=50505051


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