### Home > APCALC > Chapter 6 > Lesson 6.4.1 > Problem 6-119

The graphs of the equations ,

*,*

*, and*

Show that the area of this region is

Hint: Use horizontal rectangles.

Since we are using horizontal rectangles, the infinitely small widths of each rectangle are measured on the -axis, use

*instead of*

*.*

The bounds:

Notice that BOTH equations are written with *y* 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 -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.*