5.1 Areas and Distances

1. Find the area under the curve from 0 to 2.

      .

2. Find the exact area of the region under the graph of from 0 to 2.

    .

3. Find the exact area under the sine curve from to , where .

    .

(Since , the value what we evaluate is equal to the area.)

4. (a) Let be the area of a polygon with equal sides inscribed in a circle with radius .

      By dividing the polygon into congruent triangles with central angle , show that

      .

   (b) Show that .

      [Hint: Use Equation 3.4.2]

   (a) The area of one piece of

       consists of such pieces so the area of

   (b) Using ,

       .