LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
restart:with(plots):with(Student[Calculus1]):
ApproximateInt(x^2,x=0..1,output=plot,method=right,partition=1);
ApproximateInt(x^2,x=0..1,output=plot,method=right,partition=2);
ApproximateInt(x^2,x=0..1,output=plot,method=right,partition=4);
ApproximateInt(x^2,x=0..1,output=plot,method=right,partition=8);
ApproximateInt(x^2,x=0..1,output=plot,method=right,partition=16);
ApproximateInt(x^2,x=0..1,output=plot,method=right,partition=32);
ApproximateInt(x^2,x=0..1,output=plot,method=right,partition=64);
ApproximateInt(x^2,x=0..1,output=plot,method=left,partition=1);
ApproximateInt(x^2,x=0..1,output=plot,method=left,partition=2);
ApproximateInt(x^2,x=0..1,output=plot,method=left,partition=4);
ApproximateInt(x^2,x=0..1,output=plot,method=left,partition=8);
ApproximateInt(x^2,x=0..1,output=plot,method=left,partition=16);
ApproximateInt(x^2,x=0..1,output=plot,method=left,partition=32);
ApproximateInt(x^2,x=0..1,output=plot,method=left,partition=64);
ApproximateInt(x^2,x=0..1,output=sum,method=right,partition=n);
ApproximateInt(x^2,x=0..1,output=sum,method=left,partition=n);
limit(ApproximateInt(x^2,x=0..1,output=sum,method=left,partition=n),n=infinity);
limit(ApproximateInt(x^2,x=0..1,output=sum,method=right,partition=n),n=infinity);
ApproximateInt(sin(x),x=0..Pi,output=plot,method=left,partition=1);
ApproximateInt(sin(x),x=0..Pi,output=plot,method=left,partition=2);
ApproximateInt(sin(x),x=0..Pi,output=plot,method=left,partition=4);
ApproximateInt(sin(x),x=0..Pi,output=plot,method=left,partition=8);
ApproximateInt(sin(x),x=0..Pi,output=plot,method=left,partition=16);
ApproximateInt(sin(x),x=0..Pi,output=sum,method=left,partition=n);
limit(ApproximateInt(sin(x),x=0..Pi,output=sum,method=left,partition=n),n=infinity);
sum(1-4*i/n-4*i^2/n^2,i=1..n);
limit(2/n*sum(1-4*i/n-4*i^2/n^2,i=1..n),n=infinity);
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=