[填空题]
Let f(x)=$x(x-3)^{2}$ , for $0 \leq x \leq 4$ . The following graph shows f .
Let R be the region enclosed by f , the x -axis and the lines x=0, x=3 .
1. Show that $\int f(x) \mathrm{d} x$=$\frac{x^{4}}{4}-2 x^{3}+\frac{9 x^{2}}{2}+C$.
2. Find the volume formed when R is rotated $360^{\circ}$ about the x -axis ;The volume is given by the integral V= .
3. The diagram below shows part of the graph of the quadric function g(x)=x(a-x) . The graph of g crosses the x -axis when x=a .
The area enclosed by the graph of g is equal to the area of R . Find the value of a is .
