Let R be the region between the graphs , y = x2, and the line x = 4.
Write an integral expression for the area of R, using vertical slices.
The height of a slice is :
The area of a slice is
The variable x measures the position of the slice on the x-axis, and x ranges from 1 to 4.
The area of R is
When we go beyond finding area to finding mass, pressure, or the volume of the Batmobile, we'll need to think about things besides the shape of the region when deciding which way to slice. We're having you practice slicing every-which-way now so you'll be comfortable slicing every-whatever-way later.