The integral $$\int\limits_1^2 {{e^x}.{x^x}\left( {2 + {{\log }_e}x} \right)} dx$$ equals :

For all twice differentiable functions f : R $$ \to $$ R,
with f(0) = f(1) = f'(0) = 0

Let f : R $$ \to $$ R be a function defined by
f(x) = max {x, x²}. Let S denote the set of all points in R, where f is not differentiable. Then :

The set of all real values of $$\lambda $$ for which the function

$$f(x) = \left( {1 - {{\cos }^2}x} \right)\left( {\lambda + \sin x} \right),x \in \left( { - {\pi \over 2},{\pi \over 2}} \right)$$

has exactly one maxima and exactly one minima, is :