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If f(a+b-x)=f(x), then inta bf(x)dxis e...

If `f(a+b-x)=f(x)`, then `inta bf(x)dx`is equal to(A) `(a+b)/2inta bf(b-x)dx` (B) `(a+b)/2inta bf(b+x)dx`(C) `(b-a)/2inta bf(x)dx` (D) `(a+b)/2inta bf(x)dx`

Text Solution

Verified by Experts

Given` f(a + b - x) = f(x)`
⇒`a+b−x=x`
⇒`x=(a+b)/2​`
Let` I=∫_a^babf(x)dx =(a+b)/2∫_a^babf(x)dx`
Hence option D is correct
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