### 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 ^{\frac { 28 } { 3 }}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.*