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Show that int0af(x)g(x)dx=2int0af(x)dx i...

Show that `int0af(x)g(x)dx=2int0af(x)dx` if f and g defined as `f(x)" "=" "f(a-x)` and `g(x)" "+g(a-x)=" "4`

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`"Let I "=int_(0)^(a)f(x) g(x) dx" "....(1)`
` I=int_(0)^(a)f(a-x)g(a-x)dx`
`[ :' int_(0)^(a) f(x) dx=int_(0)^(a) f(a-x)dx]`
`rArr " "I= int_(0)^(a) f(x) {4-g(x)}dx " "....(2)`
`[ :' f(x)=f(a-x) " and " g(x)`
`+g(a-x)=4 " (given )"]`
Adding equations (1) and (2)
`rArr " "2I =int_(0)^(a) 4f(x) dx rArr I=2 int_(0)^(a) f(x) dx`
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