Homework 3

1. 10.11 Use matlab to compute the integral of the function: cos²(0.5x)sin⁴(0.5x)
   in the range [0 ... pi] Turn in the matlab command used to compute this function and the answer.
   
2. 9.1 The position a particle, moving as a function of time, is given by: x = (2+4 cos(t)) cos(t)
   y = (2+4 cos(t)) sin(t)
   z = t² Plot the position of the particle for t varying from 0 to 20. Use enough values of t that the plot looks smooth. Turn in the matlab commands used to make this plot and the plot itself.
   
   
3. 9.5 Make a 3-D surface plot and a contour plot (both in the same figure) of the function: z = (y+3)² + 1.5x² - x²y
   for values of x and y ranging from -3 to 3. (hint, use meshgrid, and look up the help for "contour" . Turn in the matlab commands used to make this plot and the plot itself.