PKšMmXñB–Hmimetypetext/x-wxmathmlPKšMmXQdBV55 format.txt This file contains a wxMaxima session in the .wxmx format. .wxmx files are .xml-based files contained in a .zip container like .odt or .docx files. After changing their name to end in .zip the .xml and eventual bitmap files inside them can be extracted using any .zip file viewer. The reason why part of a .wxmx file still might still seem to make sense in a ordinary text viewer is that the text portion of .wxmx by default isn't compressed: The text is typically small and compressing it would mean that changing a single character would (with a high probability) change big parts of the whole contents of the compressed .zip archive. Even if version control tools like git and svn that remember all changes that were ever made to a file can handle binary files compression would make the changed part of the file bigger and therefore seriously reduce the efficiency of version control wxMaxima can be downloaded from https://github.com/wxMaxima-developers/wxmaxima. It also is part of the windows installer for maxima (https://wxmaxima-developers.github.io/wxmaxima/). If a .wxmx file is broken but the content.xml portion of the file can still be viewed using an text editor just save the xml's text as "content.xml" and try to open it using a recent version of wxMaxima. If it is valid XML (the XML header is intact, all opened tags are closed again, the text is saved with the text encoding "UTF8 without BOM" and the few special characters XML requires this for are properly escaped) chances are high that wxMaxima will be able to recover all code and text from the XML file. PKšMmX{« ´b´b content.xml Kedvenc Matematikai Kísérleteim Alapok Halmazok és függvények Számok Határérték Differenciálszámítás Integrálszámítás Lineáris algrebra Többváltozós függvények Metrikus terek Differeciálszámítás Integrálszámítás Többváltozós függvények integrálja Tétel Tétel Következmény Tétel: az integrál egyértelműsége Tétel: az integrál linearitása Tétel: integrál és koordinátafüggvények Tétel: az integrál nemnegativitása Következmény: az integrál monotonitása Megjegyzés Az integrál mint téglafüggvény additivitása Tétel: határátmenet és integrál felcserélése egyenletes konvergenciánál Példa assume(n>1); (%o1) [n>1] integrate(x*(1-x^2)^n,x,0,1); (%o2) 12*

n+1

Nullahalmazok Tétel: ismételt integrálás Abszolút integrálható függvények Tétel Normál integrációs tartomány Tétel Példa: forgástest térfogata Feladat kill(all); (%o0) done assume(a>0); (%o1) [a>0] integrate(5*a/2-x-a^2/x,x,a/2,2*a); (%o2) −a2*log

2*a

+

8*log

a2

−9

*a28
+3*a2
ratsimp(%); (%o3) −8*a2*log

2*a

+

−8*log

a2

−15

*a28
%, logexpand=super; (%o4) −a2*

−8*

log

a

−log

2

−15

+8*a2*

log

a

+log

2

8
ratsimp(%); (%o5) −

16*log

2

−15

*a28
Feladat kill(all); (%o0) done integrate(1,z,0,x^2+y^2); (%o1) y2+x2 integrate(%,y,x^2,1); (%o2) 3*x2+13−x6+3*x43 integrate(%,x,-1,1); (%o3) 88105 Feladat kill(all); (%o0) done integrate(1,z,0,6-x-y); (%o1) −y−x+6 integrate(%,y,2-x/2,6-x); (%o2) x2−12*x+362−3*x2−32*x+808 ratsimp(%); (%o3) x2−16*x+648 integrate(%,x,0,8); (%o4) 643 Feladat (1) integrate(x^2+y^2,y,0,1-x); (%o1) −4*x3−6*x2+3*x−13 integrate(%,x,0,1); (%o2) 16 (2) integrate((y-x^2)^(1/2),y,x^2,4); (%o7) −4−x2*

2*x2−8

3
integrate(%,x,-2,2); (%o8) 4*%pi (3) assume(a>0); (%o1) [a>0] y=a+(a^2-(x-a)^2)^(1/2); (%o5) y=a2−

x−a

2
+a
radcan(%); (%o6) y=2*a−x*x+a integrate(2*(2*a*x-x^2)^(1/2)/(2*a-x)^(1/2),x,0,a); (%o7) 4*a323 (4) x-ben páratlan, az x szerinti integrálok nullák, így 0 etc. Feladat (1) T:integrate(f(x),x,a,b); (%o4) abf

x

dx
integrate(x*f(x),x,a,b); (%o5) abx*f

x

dx
integrate(y,y,0,f(x)); (%o6) f

x

2
2
(2) T:integrate((1-x^(1/2))^2,x,0,1); (%o8) 16 integrate(x*(1-x^(1/2))^2,x,0,1); (%o11) 130 integrate(y,y,0,(1-x^(1/2))^2); (%o12) −−x2+x*

4*x+4

−6*x−1
2
integrate(%,x,0,1); (%o13) 130 (3) solve(x^2=1-x); (%o6) [x=−5+12,x=5−12] T:integrate(1-x-x^2,x,0,(5^(1/2)-1)/2); (%o7) 532−712 Ix:integrate(x-x^2-x^3,x,0,(5^(1/2)-1)/2); (%o9) −532−1324 integrate(y,y,x^2,1-x); (%o10) x2−2*x+12−x42 Iy:integrate(%,x,0,(5^(1/2)-1)/2); (%o11) 552−4760 (4) Páros x-ben és y-ban is, így nulla (5) x^2+y^2-x-y=(x-1/2)^2+(y-1/2)^2-1/2 T:T1+T2; (%o15) T2+T1 integrate(x+y-x^2-y^2,y,0,1/2+(1/2-(x-1/2)^2)^(1/2)); (%o20) −−4*x2+4*x+1*

4*x2−4*x−1

+6*x2−6*x−1
12
T1:integrate(%,x,0,1); (%o21) 3*%pi+2496 integrate(x+y-x^2-y^2,y,1,1/2+(1/2-(x-1/2)^2)^(1/2)); (%o24) 6*x2−6*x−16−−4*x2+4*x+1*

4*x2−4*x−1

+6*x2−6*x−1
12
T2:integrate(%,x,0,1); (%o25) 3*%pi−896 fz:integrate(z,z,x^2+y^2,x+y); (%o26) y2+2*x*y+x22−y4+2*x2*y2+x42 integrate(fz,y,0,1/2+(1/2-(x-1/2)^2)^(1/2)); (%o27) −−4*x2+4*x+1*

8*x4+4*x3−6*x2−11*x−2

+30*x3−20*x2−15*x−2
60
Iz1:integrate(%,x,0,1); (%o28) 25*%pi+204960 integrate(fz,y,1,1/2+(1/2-(x-1/2)^2)^(1/2)); (%o29) 15*x4−5*x2−15*x−230−−4*x2+4*x+1*

8*x4+4*x3−6*x2−11*x−2

+30*x3−20*x2−15*x−2
60
Iz2:integrate(%,x,0,1); (%o30) 75*%pi−1722880 integrate(x*(x+y-x^2-y^2),y,0,1/2+(1/2-(x-1/2)^2)^(1/2)); (%o31) −x*

−4*x2+4*x+1*

4*x2−4*x−1

+6*x2−6*x−1

12
Ix1:integrate(%,x,0,1); (%o32) −−15*%pi+192160−15*%pi+4816012 integrate(y*(x+y-x^2-y^2),y,1,1/2+(1/2-(x-1/2)^2)^(1/2)); (%o33) 6*x2−6*x−112−−6*x4+12*x3+−4*x2+4*x+1*

4*x2−4*x−1

−6*x−1
24
Iz2:integrate(%,x,0,1); (%o34) 15*%pi−32960 Tétel: paraméteres integrálok differenciálása Feladat
PKšMmXñB–HmimetypePKšMmXQdBV55 5format.txtPKšMmX{« ´b´b ’content.xmlPK§oi