<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8" family="Arial">Visualizando Regi\303\265es de Integra\303\247\303\243o em Coordenadas Polares</Font></Text-field>

JSFH

Usando coordenadas polares LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYlLUYjNictSSNtaUdGJDYmUSJyRicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYuUSIsRidGNy9GO1Enbm9ybWFsRicvJSZmZW5jZUdGOS8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0Y5LyUqc3ltbWV0cmljR0Y5LyUobGFyZ2VvcEdGOS8lLm1vdmFibGVsaW1pdHNHRjkvJSdhY2NlbnRHRjkvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GMTYmUScmIzk1MjtGJy9GNUY5RjdGQUY3RkFGN0ZBRjdGQQ==, integre 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 sobre a regi\303\243o 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.

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Evaluate LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUklbXN1YkdGJDYlLUkjbW9HRiQ2LVEmJkludDtGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjcvJSlzdHJldGNoeUdRJXRydWVGJy8lKnN5bW1ldHJpY0dGNy8lKGxhcmdlb3BHRjwvJS5tb3ZhYmxlbGltaXRzR0Y3LyUnYWNjZW50R0Y3LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGRy1GIzYlLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR0Y8L0YzUSdpdGFsaWNGJ0ZQRlIvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1GTTYlUScmIzkzNjtGJy9GUUY3RjItSShtZmVuY2VkR0YkNiQtRiM2Ji1GTTYlUSJyRidGUEZSLUYvNi1RIixGJ0YyRjUvRjlGPC9GO0Y3Rj0vRkBGN0ZBRkNGRS9GSVEsMC4zMzMzMzMzZW1GJy1GTTYlUScmIzk1MjtGJ0ZaRjJGMkYyLUYvNi1RIn5GJ0YyRjVGOEZhb0Y9RmJvRkFGQ0ZFRkgtRk02JVEjZEFGJ0ZQRlJGMg== and Graph LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn

Area Element LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2J1EjZEFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2ZvcmVncm91bmRHUSpbMCwwLDI1NV1GJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0Y1L0Y5USdub3JtYWxGJw==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2JlEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEifkYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTi1GLDYmUSNkckYnRi9GMkY1RjgtRiw2JlEoZCYjOTUyO0YnRi9GMkY1RjhGMkY8

use DocumentTools in module() local Q, r,theta,x,y,Psi,g,G,a,b; if Do(%RadioButton0) then Q:=Int(Psi*r,[r=g(theta)..G(theta),theta=a..b]); else Q:=Int(Psi*r,[theta=g(r)..G(r),r=a..b]);end if; Do(%MathContainer16 = Q); end module; end use;

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIn5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUShkJiM5NTI7RidGL0YyRjUtRiw2JVEjZHJGJ0YvRjJGNS8lK2V4ZWN1dGFibGVHRj1GOQ==

use DocumentTools in module() local Q,r,theta,x,y,Psi,g,G,a,b; if Do(%RadioButton1) then Q:=Int(Psi*r,[theta=g(r)..G(r),r=a..b]); else Q:=Int(Psi*r,[r=g(theta)..G(theta),theta=a..b]); end if; Do(%MathContainer16 = Q); end module; end use;

, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEnJiM5MzY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYuUSI9RidGMkY0LyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGS0YyRjQ=

use DocumentTools in Do(%MathContainer17 = NULL); end use;

Value of Integral

use DocumentTools in module() local f,F,g,G,a,b,q, P, s1; if Do(%RadioButton2) then Do(%MathContainer16 = MathML[Export]("Select an area element"));return;end if; Do(G = %MathContainer19); Do(g = %MathContainer21); Do(b = %MathContainer20); Do(a = %MathContainer22); Do(P = %MathContainer17); if nops([P])=0 then Do(%MathContainer18 = MathML[Export]("Please provide an integrand")); return; end if; if nops([G])=0 then Do(%MathContainer18 = MathML[Export]("Please provide G")); return; end if; if nops([g])=0 then Do(%MathContainer18 = MathML[Export]("Please provide g")); return; end if; if nops([b])=0 then Do(%MathContainer18 = MathML[Export]("Please provide b")); return; end if; if nops([a])=0 then Do(%MathContainer18 = MathML[Export]("Please provide a")); return; end if; if Do(%RadioButton0) then s1 := {theta}; if nops(select(type,indets(g),name) minus s1)>0 then Do(%MathContainer18 = MathML[Export]("Check variable in g"));return;end if; if nops(select(type,indets(G),name) minus s1)>0 then Do(%MathContainer18 = MathML[Export]("Check variable in G"));return;end if; if not type(evalf(a),numeric) then Do(%MathContainer18 = MathML[Export]("Lower limit 'a' must be numeric"));return;end if; if not type(evalf(b),numeric) then Do(%MathContainer18 = MathML[Export]("Upper limit 'b' must be numeric"));return;end if; q := Int(P*r,[r=g..G, theta=a..b]); elif Do(%RadioButton1) then s1 := {r}; if nops(select(type,indets(g),name) minus s1)>0 then Do(%MathContainer18 = MathML[Export]("Check variable in g"));return;end if; if nops(select(type,indets(G),name) minus s1)>0 then Do(%MathContainer18 = MathML[Export]("Check variable in G"));return;end if; if not type(evalf(a),numeric) then Do(%MathContainer18 = MathML[Export]("Lower limit 'a' must be numeric"));return;end if; if not type(evalf(b),numeric) then Do(%MathContainer18 = MathML[Export]("Upper limit 'b' must be numeric"));return;end if; q := Int(P*r,[theta=g..G, r=a..b]); else return; end if; Do(%MathContainer18 = value(q)); end module; end use;

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiR0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTkYyRjw=

use DocumentTools in Do(%MathContainer19 = NULL); end use;

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTkYyRjw=

use DocumentTools in Do(%MathContainer20 = NULL); end use;

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiZ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTkYyRjw=

use DocumentTools in Do(%MathContainer21 = NULL); end use;

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTkYyRjw=

use DocumentTools in Do(%MathContainer22 = NULL); end use;

JSFH

use DocumentTools, plots in module() local F,g,G,a,b, FF, gg, GG, P, bot, top, lft, rgt, fnt, bck, s1, p1,p3,p4,p5,p6, q1,q2,q3,q4,q6, k; if Do(%RadioButton2) then Do(%Plot4 = display(textplot([0,0,"Please select an area element"],font=[TIMES,ROMAN,14]),axes=none)); return; end if; Do(FF = %MathContainer17); Do(GG = %MathContainer19); Do(gg = %MathContainer21); Do(b = %MathContainer20); Do(a = %MathContainer22); if nops([FF])=0 then Do(%Plot4 = display(textplot([0,0,"Please provide an integrand"],font=[TIMES,ROMAN,14]),axes=none));return;end if; if nops([GG])=0 then Do(%Plot4 = display(textplot([0,0,"Please provide G"],font=[TIMES,ROMAN,14]),axes=none)); return; end if; if nops([gg])=0 then Do(%Plot4 = display(textplot([0,0,"Please provide g"],font=[TIMES,ROMAN,14]),axes=none)); return; end if; if nops([b])= 0 then Do(%Plot4 = display(textplot([0,0,"Please provide b"],font=[TIMES,ROMAN,14]),axes=none)); return; end if; if nops([a])= 0 then Do(%Plot4 = display(textplot([0,0,"Please provide a"],font=[TIMES,ROMAN,14]),axes=none)); return; end if; p1 := display(textplot([0,0," "]),axes=none); p3 := display(textplot([0,0,"Check variables in g"],font=[TIMES,ROMAN,14]),axes=none); p4 := display(textplot([0,0,"Check variables in G"],font=[TIMES,ROMAN,14]),axes=none); p5 := display(textplot([0,0,"Lower limit 'a' must be numeric"],font=[TIMES,ROMAN,14]),axes=none); p6 := display(textplot([0,0,"Upper limit 'b' must be numeric"],font=[TIMES,ROMAN,14]),axes=none); F := unapply(FF,(r,theta)); if Do(%RadioButton0) then s1 := {theta}; if nops(select(type,indets(gg),name) minus s1)>0 then Do(%Plot4 = p3);Do(%Plot3 = p1);return;end if; if nops(select(type,indets(GG),name) minus s1)>0 then Do(%Plot4 = p4);Do(%Plot3 = p1);return;end if; if not type(evalf(a),numeric) then Do(%Plot4 = p5);Do(%Plot3 = p1);return;end if; if not type(evalf(b),numeric) then Do(%Plot4 = p6);Do(%Plot3 = p1);return;end if; g := unapply(gg,theta); G := unapply(GG,theta); top := plot3d([r,t,F(r,t)],r=g(t)..G(t),t=a..b,coords=cylindrical): bot := plot3d([r,t,0], r=g(t)..G(t),t=a..b,coords=cylindrical): bck := plot3d([g(t),t,z],t=a..b,z=0..F(g(t),t),coords=cylindrical): fnt := plot3d([G(t),t,z],t=a..b,z=0..F(G(t),t),coords=cylindrical): lft := plot3d([r,a,z],r=g(a)..G(a),z=0..F(r,a),coords=cylindrical): rgt := plot3d([r,b,z],r=g(b)..G(b),z=0..F(r,b),coords=cylindrical): elif Do(%RadioButton1) then s1 := {r}; if nops(select(type,indets(gg),name) minus s1)>0 then Do(%Plot4 = p3);Do(%Plot3 = p1);return;end if; if nops(select(type,indets(GG),name) minus s1)>0 then Do(%Plot4 = p4);Do(%Plot3 = p1);return;end if; if not type(evalf(a),numeric) then Do(%Plot4 = p5);Do(%Plot3 = p1);return;end if; if not type(evalf(b),numeric) then Do(%Plot4 = p6);Do(%Plot3 = p1);return;end if; g := unapply(gg,r); G := unapply(GG,r); top := plot3d([r,t,F(r,t)],t=g(r)..G(r),r=a..b,coords=cylindrical): bot := plot3d([r,t,0], t=g(r)..G(r),r=a..b,coords=cylindrical): bck := plot3d([a,t,z],t=g(a)..G(a),z=0..F(a,t),coords=cylindrical): fnt := plot3d([b,t,z],t=g(b)..G(b),z=0..F(b,t),coords=cylindrical): lft := plot3d([r,g(r),z],r=a..b,z=0..F(r,g(r)),coords=cylindrical): rgt := plot3d([r,G(r),z],r=a..b,z=0..F(r,G(r)),coords=cylindrical): else return; end if; P := display([bot,top,lft,rgt,fnt,bck],axes=box,labels=[x,y,z],orientation=[-115,80]); Do(%Plot4 = P); if Do(%RadioButton0) then q1 := plot([[g(t),t,t=a..b],[G(t),t,t=a..b],[r,a,r=g(a)..G(a)],[r,b,r=g(b)..G(b)]],coords=polar, color=[red,green,blue,blue]): q2 := animate(plot, [[k*g(t)+(1-k)*G(t),t,k=0..1],coords=polar,color="Orange",thickness=3],t=a..b,frames=25): q3 := animate(plot,[ [[g(t),t]],style=point,coords=polar, symbol=circle,color=black,symbolsize=20],t=a..b,frames=25): q4 := animate(plot,[ [[G(t),t]],style=point,coords=polar, symbol=solidcircle,color=black,symbolsize=20],t=a..b,frames=25): q6:=display([q1,q2,q3,q4],scaling=constrained,labels=[x,y]); else q1 := plot([[r,g(r),r=a..b],[r,G(r),r=a..b],[a,t,t=g(a)..G(a)],[b,t,t=g(b)..G(b)]], coords=polar, color=[red,green,blue,blue]): q2 := animate(plot, [[r,k*g(r)+(1-k)*G(r),k=0..1],coords=polar,color="Orange",thickness=3],r=a..b,frames=25): q3 := animate(plot,[ [[r,g(r)]],style=point,coords=polar, symbol=circle,color=black,symbolsize=20],r=a..b,frames=25): q4 := animate(plot,[ [[r,G(r)]],style=point,coords=polar, symbol=solidcircle,color=black,symbolsize=20],r=a..b,frames=25): q6:=display([q1,q2,q3,q4],scaling=constrained,labels=[x,y]); end if; Do(%Plot3 = q6); end module; end use;

use DocumentTools, plots in module() local p; p := display(textplot([0,0," "]),axes=none); Do(%Plot3 = p); Do(%Plot4 = p); end module; end use;

use DocumentTools, plots in module() local p; p := display(textplot([0,0," "]),axes=none); Do(%Plot3 = p); Do(%Plot4 = p); Do(%MathContainer16 = NULL); Do(%MathContainer17 = NULL); Do(%MathContainer19 = NULL); Do(%MathContainer21 = NULL); Do(%MathContainer20 = NULL); Do(%MathContainer22 = NULL); Do(%MathContainer18 = NULL); Do(%RadioButton2(value)=true); end module; end use;

Bounding Curves

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"Volume"

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2I1EhRictRiM2KEYrRitGKy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EoMkR+TWF0aEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0YrRjFGNEY3

O gr\303\241fico \303\240 esquerda \303\251 uma anima\303\247\303\243o de como o raio vetor varre a regi\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn. O gr\303\241fico \303\240 esquerda interpreta a integral como o c\303\241lculo de um volume.

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