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5. Now let’s take a look at the parametric equations x = 4 cost &y= –2 sint, where a sts in
a. (2 points) Eliminate the parameter, t, so as to yield a recognizable function of x & y only.
b. (4 points) Make a detailed sketch of this curve on your own coordinate system; be sure to indicate the direction of
increasing parameter, t. Note the bounds on the parameter, t.
C. (2 points) Set up an integral to calculate the length of this curve, but DO NOT EVALUATE IT.
d. (4 points) Use Simpson’s rule with n = 8 subintervals to approximate your integral in part (c); be sure to show your
7. Solve each of the following differential equations with the given initial conditions.
a. (5 points)
y (1 – xº) & y(2)=1
b. (5 points) Y’ + 2xy = e-z? cos & y(0) = 3
b. Find the centroid (center of mass) of the region bounded by the curves y=x? &y=x+2.
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