Assertion (A): $$\int_\limits2^8 \frac{\sqrt{10-x}}{\sqrt{x}+\sqrt{10-x}} d x=3$$

Reason (R): $$\int_\limits a^b f(x) d x=\int_a^b f(a+b-x) d x$$

Write the domain and range (principle value branch) of the following functions: $$f(x)=\tan ^{-1} x$$

(a) If $$f(x)=\left\{\begin{array}{ll}x^2, & \text { if } x \geq 1 \\ x, & \text { if } x<1\end{array}\right.$$, then show that $$f$$ is not differentiable at $$x=1$$.

OR

(b) Find the value(s) of '$$\lambda$$', if the function

$$f(x)=\left\{\begin{array}{cc} \frac{\sin ^2 \lambda x}{x^2}, & \text { if } x \neq 0 \\ 1, & \text { if } x=0 \end{array} \text { is continuous at } x=0 .\right.$$

Sketch the region bounded by the lines $$2 x+y=8, y=2, y=4$$ and the $$y$$-axis. Hence, obtain its area using integration.