approx the area of a region by making rectangnle?

Question

take graph of y=cosx on interval [0, pi/2]. create 4 rectangle at exact values to determine area between the graph of y=cosx and x-axis.

Answer 1

this is integration using approximating rectangles.
If you're using left endpoints, the first rectangle is at f(0), the second is f(pi/8), third is at f(pi/4), the last is at f(3pi/8). Sketch the cosine graph (period is 2 pi)and the rectangles, then plug in the cosine values for those numbers.

Answer 2

First, you should do your own homework, and it sounds like you are not asking for help, but the answer. The following isn't the answer, but how to go about doing the problem.

If the interval is 0 to pi/2, can you split it into four even chunks?
Do you know the value of cos(x) where x = 0? where x = pi/2?

Come up with the other values, compute cos(x) for those. The area of each rectangle is the height x width. If you split the region into 4 equal pieces, you should be able to figure out the width. If you multiply by the height, that would be the area of the rectangle.

Here's a great reference on Wikipedia:
http://en.wikipedia.org/wiki/Numerical_integration

Answer 3

Sure... or:

int(cosx)dx between 0 and pi/2
which is sin(pi/2)-sin(0)
which, since sin(0) = 0 and sin(pi/2) = 1

the area between 0 and pi/2 is 1