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Text File  |  1989-09-04  |  1.0 KB  |  32 lines
  1. "File:  INTEGRAL.MTH  (c)           09/04/89          Soft Warehouse, Inc."
  2.  
  3. "The arc length of u(x) from x=a to x=b:"
  4.  
  5. ARC_LENGTH(u,x,a,b):=INT(SQRT(1+DIF(u,x)^2),x,a,b)
  6.  
  7. "The vector arc length of v(t) from t=a to t=b:"
  8.  
  9. VECTOR_ARC_LENGTH(v,t,a,b):=INT(SQRT(SUM(DIF(ELEMENT(v,k_),t)^2,k_,1,DIMENSION~
  10. (v))),t,a,b)
  11.  
  12. "The volume of revolution of u(x) from x=a to x=b:"
  13.  
  14. VOLUME_OF_REVOLUTION(u,x,a,b):=PI*INT(u^2,x,a,b)
  15.  
  16. "The surface area of revolution of nonnegative u(x) from x=a to x=b:"
  17.  
  18. SURFACE_OF_REVOLUTION(u,x,a,b):=2*PI*INT(u*SQRT(1+DIF(u,x)^2),x,a,b)
  19.  
  20. "The Fourier series approximation of u(x) from x=a to x=b for n terms:"
  21.  
  22. FOURIER(u,x,a,b,n):=1/(b-a)*INT(u,x,a,b)+2/(b-a)*SUM(COS(2*PI*k_*x/(b-a))*INT(~
  23. u*COS(2*PI*k_*x/(b-a)),x,a,b)+SIN(2*PI*k_*x/(b-a))*INT(u*SIN(2*PI*k_*x/(b-a)),~
  24. x,a,b),k_,1,n)
  25.  
  26. "The Laplace transform of u(t) in terms of the variable s (note that s"
  27.  
  28. "must be declared large enough so that the integral will converge):"
  29.  
  30. LAPLACE(u,t,s):=INT(#e^(-s*t)*u,t,0,INF)
  31.  
  32.