Consider the area shown below. The height of the triangle is 5 and the length of its base is 3. We have used the notation for .

graph of an isosceles triangle with its base on the x-axis. a strip of width Dh is shown part of the way up the triangle, and the height from the axis to the strip designated as h.

Write a Riemann sum for the area, using the strip shown and the variable :
Riemann sum

Now write the integral that gives this area:
area
where
and

Finally, calculate the exact area of the region, using your integral.
area =

You can earn partial credit on this problem.