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Home > CALC > Chapter 6 > Lesson 6.4.1 > Problem 6-126


The graphs of the equations , , , and are shown below. These four graphs form the boundary of a region.

Show that the area of this region is un. Hint: Use horizontal rectangles.

Since we are using horizontal rectangles, the infinitely small widths of each rectangle are measured on the -axis...
hence we us instead of .

The bounds:
Notice that BOTH equations are written with as the input and as the output.
Therefore, find the bounds of integration will be on the -axis.
lower value
upper value

The integrand:
The 'top function' and 'bottom function' will also be determined with respect to the y-axis.
Let the 'top function' be the one with the right-most position, while the 'bottom function' will be the one with the 'left-most position.'
Another way to look at this is the 'top function' has the highest -values, while the 'bottom function' has the lower -values.