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 ,