SOLUTION: graph the following curves: y=x, xy=1 and x=2 and determinethe area bounded using: a)A vertical element b)A horizontal element

Sorry, I misread x=2 as y=2.  But here it is for y=2.



We must break the area into two parts, so that in each part the
ends of the elements are on the same two different curves throughout
the area.  So the green line is the dividing line.  We will find the
area of the region to the left of the green line and then find the
area of the region to the right of the green line and add them together:







The area to the right of the green line is just an isosceles right triangle
with each leg = 1 = base = height.  So the area is given by:


So the sum of the areas of the two parts are



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Now we'll do it with horizontal elements.



Using horizontal element:

We must solve the equations of xy=1 for x and y=x for x if we
use horizontal elements. They are x=1/y and x=y.

The region does not need to be broken up because one end of the
horizontal element is on y=1/x throughout the area, and the other
end of the horizontal element is on y=x throughout the area.







Edwin