The function `f` and `g` are positive and continuous. If `f` is increasing and `g` is decreasing, then `int_0^1f(x)[g(x)-g(1-x)]dx` is always non-posi

Question

The function `f` and `g` are positive and continuous. If `f` is increasing and `g` is decreasing, then `int_0^1f(x)[g(x)-g(1-x)]dx` is always non-posi

The function `f` and `g` are positive and continuous. If `f` is increasing and `g` is decreasing, then `int_0^1f(x)[g(x)-g(1-x)]dx` is always non-positive is always non-negative can take positive and negative values none of these
A. is always non-positive
B. is always non-negative
C. can take positive and negative values
D. none of these

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - A
`I=int_(0)^(1)f(x)[g(x)-g(1-x)]dx`
`=-int_(0)^(1)f(1-x)[g(x)-g(1-x)]dx`
or `2I=int_(0)^(1)[f(x)-f(1-x)][g(x)-g(1-x)]dx`
`=2int_(0)^(1//2)[f(x)-f(1-x)].[g(x)-g(1-x)]dxle0`

5 views Answered 2023-02-05 15:29