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If f(a+b-x)=f(x),\ then prove that\ int...

If `f(a+b-x)=f(x),\ ` then prove that`\ int_a^b xf(x)dx=(a+b)/2int_a^bf(x)dx`

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By property we know
`int_a^b f(x)=int_a^b f(a+b-x)`
`int_a^b xf(x)dx=int_a^b (a+b-x)f(a+b-x)dx`
`int_a^b xf(x)dx=int_a^b (a+b-x)f(x)dx`
`int_a^b xf(x)dx=int_a^b (a+b)df(x)dx-int_a^b(x)f(x)dx`
`2int_a^b xf(x)dx=int_a^b (a+b)df(x)dx`
...
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