Exercises

1. For each of the following regions of the plane, sketch the region and label its boundaries and use the FTC to compute the area of the region.
   1. The region under the graph of between 0 and 4.
   2. The region between the graphs of the function and g(x) = x/2 -3 between and .
   3. The region between the graph of and the x-axis on the interval [-2,2].
2. 1. 1. If is a point where , what does that tell us about the behavior of F at ? Explain your answer.
      2. If is a point where , what does that tell us about the behavior of F at ? Explain your answer.
      3. If is a point where , what does that tell us about the behavior of F at ? Explain your answer.
   2. 1. If is a point where , what does that tell us about the behavior of F at ? Explain your answer.
      2. If is a point where , what does that tell us about the behavior of F at ? Explain your answer.
      3. If is a point where , what does that tell us about the behavior of F at ? Explain your answer.
   3. Let . Use your calculator to graph f. Applying your answers to (a) and (b) and your knowledge of f, describe the behavior of the anti-derivative F of f with the property that F(0)=1. Use this information to plot (by hand) and label the graph of F.