Question

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`

Answer 1

Correct Answer - 5
We have `f(2x)=3f(x)`……………1
and `int_(0)^(1)f(X)dx=1` ……………..2
From equatons 1 and 2 `1/3int_(0)^(1)f(2x)dx=1`
Put `2x=t`. Then `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`