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 ,

.