Use MATLAB to solve each problem. Some of the commands you may need on this assignment are: syms, fplot, hold on, int, fimplicit, solve, and double.

Consider the equation x = -y^2 + 5y - 3

a) Use fimplicit to plot the graph of this equation for in the interval [ -2, 5]

b) Find the y-intercepts of this graph.

c) Find the volume of the solid found by rotating the region bounded by the y-axis and x = -y^2 + 5y -3 about the y-axis. USE THE DISK METHOD (even if you have already learned the shell method). [Use the double command to approximate your answer as a decimal]