## File: dblint.dm1

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maxima 5.6-17
 `123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869` ``````/* a macro for floatdefunk, needed until optimu is used */ load("fltdfnk.mc")\$ /* Example of use of double integrator (DBLINT), part 2, plus FLOATDEFUNK and QUANC8 */ /* Get the fasl file for DBLINT */ LOAD('DBLINT); /* Get the fasl file for QUANC8 */ LOAD('QQ); /* Use DBLINT to get the double integral of exp(x-y^2) over the region bounded by y=1 and y=2+x^(3/2) and x=0 to x=1 */ /* Define the integrand as a function of two variables */ F(X,Y):=(MODE_DECLARE([X,Y],FLOAT),EXP(X-Y^2)); /* Define the lower and upper limits on the inner (y in this case) integral as a function of the outer variable (x in this case) */ R(X):=(MODE_DECLARE(X,FLOAT),1.0); S1(X):=(MODE_DECLARE(X,FLOAT),2.0+X^(3/2)); /* Now translate these functions for the sake of efficiency */ TRANSLATE(F,R,S1); /* Call the DBLINT function with quoted arguments for function names, and floating point values for the endpoints of the outer (x) integration */ DBLINT_ANSWER:DBLINT('F,'R,'S1,0.0,1.0); /* Now generate the exact integral over y using RISCH */ INTY:RISCH(EXP(X-Y^2),Y); /* Now get the integrand of the x integral */ XINT:EV(INTY,Y:2+X^(3/2))-EV(INTY,Y:1); /* Try to do the x integral exactly */ RISCH(XINT,X); RADCAN(%); %,NOUNS; /* Still no luck with closed-form */ /* The integral over x can't be done in closed-form, so let's use a one-dimensional integrator to do it numerically. First, we must define the integrand as a floating point function. FLOATDEFUNK does this very conveniently on the expression */ FLOATDEFUNK(fUN,[X],XINT); /* Now translate the function fun */ TRANSLATE(FUN); /* Now call QUANC8 on the translated function (see SHARE1;QQ USAGE for details) */ QUANC8_ANSWER:QUANC8(FUN,0.0,1.0); /* Compare the answers from DBLINT and QUANC8 */ (DBLINT_ANSWER-QUANC8_ANSWER)/DBLINT_ANSWER; /* It appears to be small enough relative error for most uses */ "end of dblint.dm1"\$ ``````