maple - Shade Bounded Region along y-axis -

i plotted line want shade area between 2 , 4 along y axis illustrate area under curve cannot figure out how that, can help? code, rather simple

>y:=(2*x);  >plot(y,x=0..3); 

i find difficult understand region have in mind.

is 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 omit curve (line) y=2*x by removing call plot above.

if have other region in mind should able adjust call plots:-inequal accordingly.

there other ways accomplish such things, such calling plot filled option. can use plottools:-reflect, or use parametric calling sequence of plot, flip x , y axes.

i figure might wanting avoid having "solve x", x values corresponding y=2 , y=4 (even though in example of y=2*x can in head).

these reasons why think you'd likley find easiest use plots:-inequal.

[edit: followup comment 8 rectangles]

first, different example, 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 visualized using riemannsum command student:-calculus1 package. (or use seq command , construct them formulas corners -- seems lot of awkward bookkeeping.)

you can of course remove of parts passed below 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 little less complicated if wanted area between curve , x-axis instead.