Accumulated cross-sections

[walker799]

Redundancy in the textbook:

Since we are slicing with respect to x
, we must express the side length s
in terms of x
. Thus, we describe the curves in the image as functions of x
.

Note that the parabola x=4−y2
must be described using
2
functions of x
. In fact, solving for y
, we obtain y=+
sqrt(4-x)
and y=−
sqrt(4-x)
.

Note that the parabola x=4−y2
does not pass the vertical line test, so it must be described using
2
functions of x
. This also arises as an algebraic consequence when we solve for y
since we must consider the positive and negative square roots. In fact, solving for y
gives y=+
sqrt(4-x)
and y=−
sqrt(4-x)
.>

See accumulatedCrossSections/digInAccumulatedCrossSections.tex