Question

Sketch the regions enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. integrate with either respect to x or y, then find area S of the region given that y=sqrt(x), y=x/2, and x=9 ?

Answer 1

View sketch:
http://img508.imageshack.us/img508/4421/1287636971.png

You will notice that the region enclosed by the three curves is a triangular region whose vertices are the intersections (4,2), (9,3) and (9,4.5), which gives the base and height as 1.5 and 5, or 3.75 for the area.

I can see that it is easier to integrate from x=4 to x=9, as there will be only two curves (sqrt(x) and x/2) involved for each slice.

Try your integration and post your answer for checking if you wish. The numerical answer is less than 3.6.