Shade Bounded Region along y-axis

Question

I plotted a line but want to shade the area between 2 and 4 along the y axis to illustrate area under the curve but cannot figure out how to do that, can anyone help? This is the code, which is rather simple

>y:=(2*x);

>plot(y,x=0..3);

Answer 1

I find it difficult to understand just what region you have in mind.

Is it this?

restart;

y := 2*x:

plots:-display(
  plot(2*x, x=0..3),
  plots:-inequal([Y>=y, Y>=2, Y<=4], x=0..3, Y=0..6,
                 'nolines', 'color'="Burgundy")
);

Of course you could omit the curve (line) y=2*x by removing the call to plot above.

If you have some other region in mind then you should be able to adjust the call to plots:-inequal accordingly.

There are other ways to accomplish such things, such as calling plot with its filled option. You can also use plottools:-reflect, or use the parametric calling sequence of plot, to flip x and y axes.

I figure that you might be wanting to avoid having to "solve for x", to get x values corresponding to y=2 and y=4 (even though in this example of y=2*x you can do that in your head).

These are reasons why I think you'd likley find it easiest to just use plots:-inequal.

[edit: for followup comment about 8 rectangles]

First, a slightly different example, hopefully for more clarity.

restart;

x:=arcsin(y/6):

P := plots:-display(
  plot(x, y=2..5),
  plots:-inequal([X<=x], y=2..5, X=0..1.2,
                 'nolines', 'color'=pink)
):

plots:-display(
  plot(2, color=black, linestyle=dot),
  plot(5, color=black, linestyle=dot),
  plot([x, y, y=0..6]),
  plottools:-transform((x,y)->[y,x])(P),
  view=[0..1.2,0..6],
  labels=["x","y"],
  size=[500,300]
);

The upper of lower sums (using rectangles) can be visualized using the RiemannSum command from the Student:-Calculus1 package. (Or you could use the seq command and construct them all by formulas for their corners -- but that just seems like a lot of awkward bookkeeping.)

You can of course remove any of the parts passed below to the plots:-display command.

restart;

with(Student:-Calculus1):

x:=arcsin(y/6):

P:=RiemannSum(x, y=2..5, method = upper, output = plot,
              partition=8,
              boxoptions=[filled=[color=pink,transparency=.5]],
              caption=""):

rP:=plottools:-transform((x,y)->[y,x])(P):

plots:-display(
  plot(2, color=black, linestyle=dot),
  plot(5, color=black, linestyle=dot),
  plot([x, y, y=0..6]),
  rP,
  view=[0..1.2,0..6],
  labels=["x","y"],
  size=[500,300]
);

Or,

restart;

with(Student:-Calculus1):

x:=arcsin(y/6):

P:=RiemannSum(x, y=2..5, method = lower, output = plot,
              partition=8,
              boxoptions=[filled=[color=pink,transparency=.5]],
              caption=""):

rP:=plottools:-transform((x,y)->[y,x])(P):

plots:-display(
  plot(2, color=black, linestyle=dot),
  plot(5, color=black, linestyle=dot),
  plot([x, y, y=0..6]),
  rP,
  view=[0..1.2,0..6],
  labels=["x","y"],
  size=[500,300]
);

All these examples would be a little less complicated if you wanted the area between the curve and the x-axis instead.