Problem:
Using Maple and the method of Riemann Sums, evaluate the integral
Visualization:
Right-hand endpoints:
> f := x-> x^2+3*x;
> deltax:=(3-(-1))/n;
> sum(f(-1+i*deltax)*deltax,i=1..n);
> simplify(");
> limit(", n=infinity);
Left-hand endpoints:
> sum(f(-1+(i-1)*deltax)*deltax,i=1..n);
> simplify(");
> limit(", n=infinity);
Midpoints:
> sum(f(-1+(i-1/2)*deltax)*deltax,i=1..n);
> simplify(");
> limit(", n=infinity);