Calculus-Sec-5-1-Solution 5.1   Sequences and Series                by SGLee - HSKim- SWSun  http://youtu.be/Y_nCn76RPmY

1. Find the area under the curve from 0 to 2. We divide the interval [0,2] into n equal parts.

Thus the length of each sub-interval is 2/n and the th sub-interval is given by Now we apply the right end formula to find required area.        . 2. Find the area of the region under the graph of from 0 to 2.  .

3. Find the area under the 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  Remark: To estimate area under the graph of , one can take the sample point as the point such that  .

Similarly we can choose the sample point as the point such that .

(b) Using ,  (Let . Then implies .) Think of the lower and upper sums of the graph. 