When we do substitution in definite integral evaluation do we need to make sure that the function from the integrand which is being substituted for must be bijective in the given limit of def integral or just one-one (injective) behaviour is all whats needed in the substituing function ?
Like for example in the substiution in case of integral from $\int_{0}^{2} \frac{lnx}{√(2x-x^2)}$ we cannot let $2x-x^2$ [substituing function ] to be new variable z because in the given limits it not bijective but one can break in into two regions of 0 to 1 and 1 to 2 in these regions the bijectivity behaviour is showned by $(2x-x^2)$ and then we can use it in that regions and evaluate separately .