A continuous real function `f` satisfies `f(2x)=3(f(x)AAx in RdotIfint_0^1f(x)dx=1,` then find the value of `int_1^2f(x)dx`
A continuous real function `f` satisfies `f(2x)=3(f(x)AAx in RdotIfint_0^1f(x)dx=1,` then find the value of `int_1^2f(x)dx`
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We have `f(2x)=3f(x)` and `int_(0)^(1)f(x)dx=1`
`:.1/3 int_(0)^(1)f(2x)dx=1`
Put `2x=t`
`:.1/6int_(0)^(2)f(t)dt=1`
or `int_(0)^(2)f(t)dt=6`
or `int_(0)^(1)f(t)dt+int_(1)^(2)f(t)dt=6`
Hence `int_(1)^(2)f(t)dt=6-int_(0)^(1)f(t)dt=6-1=5`
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