[问答题]
Let $y=\left(x^{2}+x\right)^{\frac{s}{2}}$ , for $x \geq 0$ .
1. Find $ \frac{\mathrm{d} y}{\mathrm{~d} x}$ .
2. Hence find $\int(2 x+1) \sqrt{x^{2}+x} \mathrm{~d} x$.
Consider the functions $ f(x)=\frac{1}{4} \sqrt{x^{2}+x}$ and $g(x)=5-\frac{x}{2} \sqrt{x^{2}+x}$ , for $x \geq 0$ . The graphs of f and g are shown in the following diagram.
The shaded region S is enclosed by the graph of f , the graph of g , the y -axis and the line x=2 .
3. Write down an expression for the area of S .
4. Hence find the exact area of S .
