kilencedik

> with(student);

[D, Diff, Doubleint, Int, Limit, Lineint, Product, Sum, Tripleint, changevar, completesquare, distance, equate, integrand, intercept, intparts, leftbox, leftsum, makeproc, middlebox, middlesum, midpoi...[D, Diff, Doubleint, Int, Limit, Lineint, Product, Sum, Tripleint, changevar, completesquare, distance, equate, integrand, intercept, intparts, leftbox, leftsum, makeproc, middlebox, middlesum, midpoi...

> f:=x->x^7*ln(x)+x-cos(x);

f := proc (x) options operator, arrow; x^7*ln(x)+x-cos(x) end proc

> g:=x->exp(-x^2);

g := proc (x) options operator, arrow; exp(-x^2) end proc

> h:=x->exp(x)*sin(x);

h := proc (x) options operator, arrow; exp(x)*sin(x) end proc

> evalf(int(f(x),x=2..3));

783.5712461

> evalf(int(g(x),x=-1..1));

1.493648266

> evalf(int(h(x),x=0..Pi));

12.07034632

> middlebox(f(x),x=2..3);

[Plot]

> evalf(middlesum(f(x),x=2..3,10));

781.0907780

> evalf(simpson(f(x),x=2..3,100));

783.5712470

> middlebox(g(x),x=-1..1,10);

[Plot]

> evalf(middlesum(g(x),x=-1..1));

1.509195888

> evalf(simpson(g(x),x=-1..1,100));

1.493648269

> middlebox(h(x),x=0..Pi,10);

[Plot]

> evalf(middlesum(h(x),x=0..Pi));

12.66778405

> evalf(simpson(h(x),x=0..Pi,100));

12.07034606

> teglalap:=proc(f,a,b,n)
local h,d;
h:=(b-a)/n;
d:=(b-a)/n*sum(f(a-h/2+i*h),i=1..n);
return evalf(d);
end proc;

>

teglalap := proc (f, a, b, n) local h, d; h := (b-a)/n; d := (b-a)*(sum(f(a-1/2*h+i*h), i = 1 .. n))/n; return evalf(d) end proc

> teglalap(f,2,3,10);

781.0907781

> with(Student[Calculus1]);

[AntiderivativePlot, ApproximateInt, ArcLength, Asymptotes, Clear, CriticalPoints, DerivativePlot, ExtremePoints, FunctionAverage, FunctionChart, GetMessage, GetNumProblems, GetProblem, Hint, Inflecti...[AntiderivativePlot, ApproximateInt, ArcLength, Asymptotes, Clear, CriticalPoints, DerivativePlot, ExtremePoints, FunctionAverage, FunctionChart, GetMessage, GetNumProblems, GetProblem, Hint, Inflecti...[AntiderivativePlot, ApproximateInt, ArcLength, Asymptotes, Clear, CriticalPoints, DerivativePlot, ExtremePoints, FunctionAverage, FunctionChart, GetMessage, GetNumProblems, GetProblem, Hint, Inflecti...

> ApproximateInt(f(x),x=2..3);

5/2+271818611107/12800000000*ln(43/20)-1/10*cos(9/4)-1/10*cos(43/20)-1/10*cos(41/20)-1/10*cos(11/4)-1/10*cos(53/20)-1/10*cos(51/20)-1/10*cos(49/20)-1/10*cos(47/20)-1/10*cos(59/20)-1/10*cos(57/20)+2488...5/2+271818611107/12800000000*ln(43/20)-1/10*cos(9/4)-1/10*cos(43/20)-1/10*cos(41/20)-1/10*cos(11/4)-1/10*cos(53/20)-1/10*cos(51/20)-1/10*cos(49/20)-1/10*cos(47/20)-1/10*cos(59/20)-1/10*cos(57/20)+2488...

>