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

The graphs of the equations

*x*=*y*^{2},*x*=*y*−1,*y*= 2, and*y*= −2 are shown below. These four graphs form the boundary of a region. Homework Help ✎Show that the area of this region is

^{}un^{2}. Hint: Use horizontal rectangles.

*dy*:

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

hence we us *dy* instead of *dx*.

The bounds:

Notice that BOTH equations are written with *y* as the input and *x* as the output.

Therefore, find the bounds of integration will be on the *y*-axis. *A* = lower *y* value *B* = upper *y* 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 *x*-values, while the 'bottom function' has the lower *x*-values.