Integrate the function”, f_]), Show([“Integrating the function”, f_, “with respect to variable”, u, “we get”, INT(f_,u)]), Display([“Considering the limits of integration for this variable, we get”,I1_]), Display([“Integrating the function”, I1_, “with respect to variable”, v, “we get”, INT(I1_,v)]), Show([“Considering the limits of integration for this variable, we get”,I2_]), Display([“Finally, integrating this result with respect to variable”, w, “the outcome is”, INT(I2_,w)]), Display(“Considering the limits of integration, the final outcome is”) ) ), I1_:=INT(I2_,w,w1,w2), If((DNQX disodium salt medchemexpress POSITION(x,VARIABLES(I1_)) or POSITION(y,VARIABLES(I1_)) or POSITION(z,VARIABLES(I1_)) or POSITION(u,VARIABLES(I1_)) or POSITION(v,VARIABLES(I1_)) or POSITION(w,VARIABLES(I1_))) /=false, RETURN [I1_,”WARNING!: SUSPICIOUS Result. Perhaps THE INTEGRATION ORDER IS Incorrect OR THE VARIABLES Modify HAS NOT BEEN Accomplished Within the LIMITS OF INTEGRATION”] ), RETURN I1_TripleSpherical(f,u,u1,u2,v,v1,v2,w,w1,w2,myTheory:=Theory, myStepwise:=Stepwise,myx:=x,myy:=y,myz:=z,f_,I1_,I2_):= Prog( f_:= rho^2 cos(phi) SUBST(f, [myx,myy,myz], [rho cos(phi) cos(theta), rho cos(phi) sin(theta), rho sin(phi)]), If(myTheory, Prog( Show(“Spherical coordinates are valuable when the expression x^2y^2z^2 appears inside the function to be integrated”), Display(“or inside the region of integration.”), Show(“A D-Fructose-6-phosphate disodium salt Endogenous Metabolite triple integral in spherical coordinates is computed by suggests of three definite integrals within a given order.”), Show(“Previously, the modify of variables to spherical coordinates has to be done.”) ) ), I1_:=INT(f_,u,u1,u2), I2_:=INT(I1_,v,v1,v2), If (myStepwise, Prog( Show([“Let us consider the spherical coordinates change”, myx, “=rho cos(phi) cos(theta)”, myy, “=rho cos(phi) sin(theta)”, myz, “=rho sin(phi)”]), Display([“The very first step will be the substitution of this variable transform in function”, f, “and multiply this outcome by the Jacobian rho^2 cos(phi).”]), Show([“In this case, the substitutions cause integrateMathematics 2021, 9,26 of)the function”, f_]), Display([“Integrating the function”, f_, “with respect to variable”, u, “we get”, INT(f_,u)]), Show([“Considering the limits of integration for this variable, we get”,I1_]), Show([“Integrating the function”, I1_, “with respect to variable”, v, “we get”, INT(I1_,v)]), Show([“Considering the limits of integration for this variable, we get”,I2_]), Display([“Finally, integrating this outcome with respect to variable”, w, “the outcome is”, INT(I2_,w)]), Show(“Considering the limits of integration, the final outcome is”) ) ), I1_:=INT(I2_,w,w1,w2), If((POSITION(x,VARIABLES(I1_)) or POSITION(y,VARIABLES(I1_)) or POSITION(z,VARIABLES(I1_)) or POSITION(u,VARIABLES(I1_)) or POSITION(v,VARIABLES(I1_)) or POSITION(w,VARIABLES(I1_))) /=false, RETURN [I1_,”WARNING!: SUSPICIOUS Result. Possibly THE INTEGRATION ORDER IS Wrong OR THE VARIABLES Adjust HAS NOT BEEN Completed In the LIMITS OF INTEGRATION”] ), RETURN I1_Appendix A.three. Location of a Region R R2 Location(u,u1,u2,v,v1,v2,myTheory:=Theory,myStepwise:=Stepwise):= Prog( If(myTheory, Show(“The area of a region R is often computed by means on the double integral of function 1 more than the region R.”) ), If(myStepwise, Display(“To get a stepwise remedy, run the program Double with function 1.”) ), If(myTheory or myStepwise, Display(“The location is:”) ), RETURN Double(1,u,u1,u2,v,v1,v2,false,false) ) AreaPolar(u,u1,u2,v,v1,v2,myTheory:=Theory,myStepwise:=Stepwise, myx:=x,myy:=y):= Prog( If(myTheory, DISPL.
