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- "File INT_APPS.MTH, copyright (c) 1990-2000 by Texas Instruments Incorporated"
-
- LAPLACE(y,t,s):=INT(#e^(-s*t)*y,t,0,inf)
-
- FOURIER(y,t,t1,t2,n):=1/(t2-t1)*INT(y,t,t1,t2)+2/(t2-t1)*SUM(COS(2*pi*m_*t/(t2~
- -t1))*INT(y*COS(2*pi*m_*t/(t2-t1)),t,t1,t2)+SIN(2*pi*m_*t/(t2-t1))*INT(y*SIN(2~
- *pi*m_*t/(t2-t1)),t,t1,t2),m_,1,n)
-
- default1:=1
-
- PARA_ARC_LENGTH(v,t,t1,t2,default1):=INT(default1*SQRT(SUM(DIF(v SUB m_,t)^2,m~
- _,1,DIMENSION(v))),t,t1,t2)
-
- ARC_LENGTH(y,x,x1,x2,default1):=PARA_ARC_LENGTH([x,y],x,x1,x2,default1)
-
- POLAR_ARC_LENGTH(r,theta,theta1,theta2,default1):=INT(default1*SQRT(r^2+DIF(r,~
- theta)^2),theta,theta1,theta2)
-
- AREA(x,x1,x2,y,y1,y2,default1):=INT(INT(default1,y,y1,y2),x,x1,x2)
-
- AREA_CENTROID(x,x1,x2,y,y1,y2,default1):=[AREA(x,x1,x2,y,y1,y2,x*default1),ARE~
- A(x,x1,x2,y,y1,y2,y*default1)]/AREA(x,x1,x2,y,y1,y2,default1)
-
- AREA_INERTIA(x,x1,x2,y,y1,y2,default1):=[[AREA(x,x1,x2,y,y1,y2,y^2*default1),A~
- REA(x,x1,x2,y,y1,y2,-x*y*default1)],[AREA(x,x1,x2,y,y1,y2,-x*y*default1),AREA(~
- x,x1,x2,y,y1,y2,x^2*default1)]]/AREA(x,x1,x2,y,y1,y2,default1)
-
- POLAR_AREA(r,r1,r2,theta,theta1,theta2,default1):=INT(INT(default1*r,r,r1,r2),~
- theta,theta1,theta2)
-
- SURFACE_AREA(z,x,x1,x2,y,y1,y2,default1):=INT(LIM(INT(default1*SQRT(1+DIF(z,x)~
- ^2+DIF(z,y)^2),y,LIM(y1,x,x_),LIM(y2,x,x_)),x_,x),x,x1,x2)
-
- VOLUME(x,x1,x2,y,y1,y2,z,z1,z2,default1):=INT(INT(INT(default1,z,z1,z2),y,y1,y~
- 2),x,x1,x2)
-
- VOLUME_CENTROID(x,x1,x2,y,y1,y2,z,z1,z2,default1):=[VOLUME(x,x1,x2,y,y1,y2,z,z~
- 1,z2,x*default1),VOLUME(x,x1,x2,y,y1,y2,z,z1,z2,y*default1),VOLUME(x,x1,x2,y,y~
- 1,y2,z,z1,z2,z*default1)]/VOLUME(x,x1,x2,y,y1,y2,z,z1,z2,default1)
-
- VOLUME_INERTIA(x,x1,x2,y,y1,y2,z,z1,z2,default1):=[[VOLUME(x,x1,x2,y,y1,y2,z,z~
- 1,z2,(y^2+z^2)*default1),VOLUME(x,x1,x2,y,y1,y2,z,z1,z2,(-x*y)*default1),VOLUM~
- E(x,x1,x2,y,y1,y2,z,z1,z2,(-x*z)*default1)],[VOLUME(x,x1,x2,y,y1,y2,z,z1,z2,(-~
- x*y)*default1),VOLUME(x,x1,x2,y,y1,y2,z,z1,z2,(x^2+z^2)*default1),VOLUME(x,x1,~
- x2,y,y1,y2,z,z1,z2,(-y*z)*default1)],[VOLUME(x,x1,x2,y,y1,y2,z,z1,z2,(-x*z)*de~
- fault1),VOLUME(x,x1,x2,y,y1,y2,z,z1,z2,(-y*z)*default1),VOLUME(x,x1,x2,y,y1,y2~
- ,z,z1,z2,(x^2+y^2)*default1)]]/VOLUME(x,x1,x2,y,y1,y2,z,z1,z2,default1)
-
- SPHERICAL_VOLUME(r,r1,r2,theta,theta1,theta2,phi,phi1,phi2,default1):=INT(INT(~
- INT(default1*r^2*SIN(theta),phi,phi1,phi2),theta,theta1,theta2),r,r1,r2)
-
- CYLINDRICAL_VOLUME(r,r1,r2,theta,theta1,theta2,z,z1,z2,default1):=INT(INT(INT(~
- default1*r,r,r1,r2),theta,theta1,theta2),z,z1,z2)
-
- VOLUME_OF_REVOLUTION(y,x,x1,x2):=CYLINDRICAL_VOLUME(r_,0,y,theta_,0,2*pi,x,x1,~
- x2)
-
- AREA_OF_REVOLUTION(y,x,x1,x2):=2*pi*PARA_ARC_LENGTH([x,y],x,x1,x2,y)
-
- VOLUMEY_OF_REVOLUTION(y,x,x1,x2):=2*pi*INT(x*y,x,x1,x2)
-
- AREAY_OF_REVOLUTION(y,x,x1,x2):=2*pi*PARA_ARC_LENGTH([x,y],x,x1,x2,x)