Area between 2D cartesian curves, fill between two ordinates, for calculus

Questions
,
1

I have not been successful in finding Help information for shading the area between two 2D cartesian curves, from one ordinate x-value to another. For example, displaying graphically the filled area between the graph of y=sinx and y=cosx from x=?/4 to x= 5?/4. Or the filled area between the graph of y=sinx and the x-axis from x=?/4 to x= 5?/4.

2

On the help page for Filling scroll down and click on Scope and then on FillingStyle and it gives the first example

Plot[{Sin[x], Cos[x]}, {x, Pi/4, 5 Pi/4}, Filling->{1->{{2}, Yellow}}]
3

Thank you Bill. What I would like to do is shade just the area from ?/4 to 5?/4, for domain 0 to 2?. My code so far as follows:

Plot[{Sin[x], Cos[x]}, {x, 0, 2 Pi}, Filling -> {1 -> {2}}, 
 FillingStyle -> Yellow, AxesLabel -> {"x", "y"}, 
 Ticks -> {{Pi/4, 5 Pi/4, 2 Pi}, {-1,  1}}, 
 GridLines -> {{{Pi/4, {Red, Dashed, 
      Thickness[0.003]}}, {5 Pi/4, {Red, Dashed, Thickness[0.003]}}, 
    2 Pi}, {-1, -Sqrt[2]/2, Sqrt[2]/2, 1}}]
4

There certainly might be a better way of doing this, but does this give you enough of a hint that you can modify this to get what you are looking for?

Show[{
  Plot[{Sin[x], Cos[x]}, {x, 0, Pi/4}, PlotRange -> {{0, 2 Pi}, {-1.01, 1}}],
  Plot[{Sin[x], Cos[x]}, {x, Pi/4, 5 Pi/4}, Filling -> {1 -> {2}}, 
   FillingStyle -> Yellow, AxesLabel -> {"x", "y"}, 
   Ticks -> {{Pi/4, 5 Pi/4, 2 Pi}, {-1, 1}}, 
   GridLines -> {{{Pi/4, {Red, Dashed, 
        Thickness[0.003]}}, {5 Pi/4, {Red, Dashed, Thickness[0.003]}},
       2 Pi}, {-1, -Sqrt[2]/2, Sqrt[2]/2, 1}}],
  Plot[{Sin[x], Cos[x]}, {x, 5 Pi/4, 2 Pi}]
}]
5

Thank you, very valuable, will continue my efforts.

6

You can find the dynamic sweeping area with the following code. It basically lay the filled area above the plot with curves only

Manipulate[
 Show[
  Plot[{Sin[x], Cos[x]}, {x, Pi/4, k}, 
   Filling -> {1 -> {{2}, Yellow}}], 
  Plot[{Sin[x], Cos[x]}, {x, Pi/4, 5 Pi/4}], 
  PlotRange -> {{Pi/4, 5 Pi/4}, {-1, 1}}, Axes -> None,
  Epilog -> 
   Inset[Row[{"Area is:", 
      NIntegrate[Sin[x] - Cos[x], {x, Pi/4, k}]}], {2.1, 0.1}]
  ], {k, Pi/4 + 0.001, 5*Pi/4}]

7933test.gif

7

Thank you Shenghui, beautiful.