If I1=∫10(1−x50)100dx and I2=∫10(1−x50)101dx such that I2=αI1 then α equals to:
I1=∫10(1−x50)100dx
I2=∫10(1−x50)(1−x50)100dx
=∫10(1−x50)100dx−∫10x50(1−x50)100dx
I2=I1−∫10xI⋅x49(1−x50)100IIdx
By using by parts
1−x50=t
⇒x49dx=−dt50
I2=I1−[x(−150)(1−x50)101101]10+∫01(−150)(1−x50)101101dx
I2=I1−0+∫10(1−x50)101(−5050)
I2=I1−I25050
50515050I2=I1
I2=50505051I1
α=50505051