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If f(x) is a function satisfying f(x+a)+...

If `f(x)` is a function satisfying `f(x+a)+f(x)=0` for all `x in R` and positive constant `a` such that `int_b^(c+b)f(x)dx` is independent of `b ,` then find the least positive value of `c`

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Verified by Experts

The correct Answer is:
`2a`
`f(x+a)+f(x)=0`
or `f(x+2a)+f(x+a)=0`
or `f(x)=f(x+2a)`
Thus, `f(x)` is periodic with period `2a`
Since `int_(b)^(c+b)f(x)dx` is independent of `b` then `c` must be `k(2a)` wher `k epsilon N`.
Hence least positive value of `c` is `2a`.
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