1.

f:[0,1)toR be a non increasing function the for alpha epsilon(0,1)

Answer»

`alpha int_(0)^(1)f(x) DX le int_(0)^(alpha)f(x)dx`
`alpha int_(0)^(1)f(x)dx ge int_(0)^(alpha)f(x)dx`
`alpha^(2) int_(0)^(1)f(x)dxleint_(0)^(alpha) f(x)dx`
`sqrt(alpha) int_(0)^(1)f(x)dxgeint_(0)^(alpha)f(x)dx`

Solution :`int_(0)^(alpha) f(x)dx`………..1
Put `x=alphat`
`:. int_(0)^(alpha) f(x)dx=alpha int_(0)^(1)f (alpha t)dt ge alpha int_(0)^(1)f(t)dt` as `alpha epsilon(0,1)`
ALSO `alpha int_(0)^(1) f(t)dt ge alpha^(2) int_(0)^(1)f(t)dt`
`:. int_(0)^(alpha)f(x)dxgealpha^(2)int_(0)^(1)f(x)dx`


Discussion

No Comment Found

Related InterviewSolutions