Wolfram Mathematica Integration techniques Roger Wells​ 2023 July Mathematicians welcome . . . all others . . . BOW YOUR HEADS!​​​
∫x^4+3x-
1
x
​​
Integrate[x^4+3x-1/x,x]
Still working on how to make the Plus C appear
​​
3
2
x
2
+
5
x
5
-Log[x]
​​​
Integrate
4
x
+3x-
1
x
,x,GeneratedParametersC
​​
Integrate
:Unknown option GeneratedParameters in Integrate-
1
x
+3x+
4
x
,x,GeneratedParametersC.
​​​Symbolic Computer Algebra​​
Integrate[a
2
x
+bx+c,x]
Quadratic roots, discriminant, directrix plots . . . very powerful.​​
cx+
b
2
x
2
+
a
3
x
3
​​​
Integrate[Sin[x]^2*Cos[x],x]
​​
3
Sin[x]
3
Integrate the function
2
sin
(x) cos (x) dx​​
Trex:=
3
Sin[x]
3
and plot the new function calling it . . .​ Trex
Plot[Trex,{x,0,2∏}]
​​​
Using the assignment operator Trex :=
Plot
3
Sin[x]
3
,{x,-8,8}
Learn the tools and artwork. Aspect Ratio Golden Ratio RANGE in mathematica does mean the typical “y” value (the ordinate) and Domain (from algebra . . . “abscissa”) is a set or list of arguments . . . the x axis. Be prudent on this to make great scientific documents, with pleasing and elegant mathematical arguments . . . for the human eye.​ Wolfram mathematica ​
Shift + drag midpoint (not corner) handle to stretch and shrink plot​
Plot
3
Sin[x]
3
,{x,0,2Pi},AspectRatio2
Using the Aspect Ratio of 2 means the Range to Domain ratio is two to one This is what it means to say a movie has been formated to your screen. In fact a television movie is usualy “formated” the other way around . . . width to hieghth. An aspect Ratio of 1 means square 1 x 1 This of course is the perfect “ picture” for exact math functions . . . “one to one”. Typos intended. And of course the Golden Ratio which is how mathematica displays a plot by default is
1+√5
2
The abscissa to ordinate ratio ​Continue to explore a function by re-naming it . . . Z ​ Z : =
1-Cos[
2
π
]
π
​​Plot [ Z ] { x , 0 , 2 Pi } ] Wolfram mathematica ​​​
​​​​Determine the integral from minus 2 π and 2 π for the function Sine ( π x ) dx.​​
π
∫
0
Sin[πx]x
Plot
1-Cos[
2
π
]
π
,{x,-2Pi,2*Pi},AspectRatio1
​​
1-Cos[
2
π
]
π
Plot
1-Cos[
2
π
]
π
,{x,-2Pi,2*Pi},AspectRatio12
​
​
Plot
1-Cos[
2
π
]
π
,{x,-2Pi,2*Pi},AspectRatio2
f[x_]:=
2
x
g[x_]:=2x
Plot[f[x],{x,0,4}]