(a) Find the volume of the region that lies inside z = x2 + y² and below the plane z = 16.[6 marks] ) Solve the following differential equations subject

to the given conditions: \text { (i) } v \frac{d v}{d x}=\frac{3}{(x+1)^{2}}, \text { with } v=2 \text { when } x=0 =) Solve the following integral problem: \int \frac{2 x+10}{x^{2}-2 x-3} d x 2 x y+\left(x^{2}+1\right) \frac{d y}{d x}=x \cos \left(x^{2}\right), \text { with } y=5 \text { when } x=0