Review for Chapter 9 and 11 Test

9.1

Set up an integral to find the arclength of a curve.  If the integral isn't too ugly, work it out.

9.2

Set up an integral to find the area of a surface obtained by rotating a curve around an axis (x-axis or y-axis).  If the integral isn't too ugly, work it out.  Infinitely long curves (such as the Gabriel's Horn problem) are fair game.  So are improper integrals (if they're not too ugly!)

9.3 

1.  You need to be able to set up (and possibly work out) hydrostatic force problems.  Your answers may be left in terms of the constants r and g (if units are meters) or d (if units are feet).

11.1 & 11.2

1.  Eliminate the parameter to find a Cartesian equation of a parametric curve.  Restrict your domain if necessary.  Sketch the curve if it's not too ugly (parabola, circle, ellipse, hyperbola, exponential are reasonable) and indicate direction.

2.  Find first and second derivatives of parametric curves.

3.  Determine at which points the curve has horizontal or vertical tangents (or tangents with a specified slope)

4.  Find the equation of the line tangent to the curve at a point.

5.  Find intervals of increase/decrease, or intervals of concavity.

6.  Find the area under a parametric curve or the area enclosed by a parametric curve.

7.  Set up an integral to find the length of a parametric curve.  Do the integral if it's not too ugly.

8.  Set up an integral to find the surface area formed by revolving a parametric curve around an axis.  Do the integral if it's not too ugly.