Source: math1110-summer2014-riemann_sums.mw 

>	# Load the Calculus1 subpackage of the Student package. # This contains the "RiemannSum" command that we'll use. with(Student[Calculus1]):

 

For more details about the RiemannSum command check out Maple's help... 

>	? RiemannSum

 

Let's compute the right hand rule approximation of    using rectangles. Then we'll find a decimal approximation of this sum and Maple's approximation of the integral. 

>	RiemannSum(cos(x), x=-Pi..2*Pi, method = right, partition=10);

 

(1)

 

>	evalf(RiemannSum(cos(x), x=-Pi..2*Pi, method = right, partition=10));

 

(2)

 

>	Int(cos(x),x=-Pi..2*Pi) = evalf(int(cos(x),x=-Pi..2*Pi));

 

(3)

 

>	RiemannSum(cos(x), x=-Pi..2*Pi, method = right, output = plot, partition=10);

 

Let's compute the left hand rule approximation of    using rectangles. Then we'll find a decimal approximation of this sum and Maple's approximation of the integral. 

>	RiemannSum(sin(x^2), x=0..1, method = left, partition=5);

 

(4)

 

>	evalf(RiemannSum(sin(x^2), x=0..1, method = left, partition=5));

 

(5)

 

>	Int(sin(x^2),x=0..1) = evalf(int(sin(x^2),x=0..1));

 

(6)

 

>	RiemannSum(sin(x^2), x=0..1, method = left, output = plot, partition=5);

 

Let compute the midpoint rule approximation of    using rectangles. We'll also find Maple's approximation and make the RiemannSum command display the sum in summation notation and make a nice plot. 

>	RiemannSum(exp(-x^2), x=-2..2, method = midpoint, partition=10);

 

(7)

 

>	evalf(RiemannSum(exp(-x^2), x=-2..2, method = midpoint, partition=10));

 

(8)

 

>	Int(exp(-x^2),x=-2..2) = evalf(int(exp(-x^2),x=-2..2));

 

(9)

 

>	RiemannSum(exp(-x^2), x=-2..2, method = midpoint, output = sum, partition=10);

 

(10)

 

>	RiemannSum(exp(-x^2), x=-2..2, method = midpoint, output = plot, partition=10);

 

Maple will also allow non-uniform partitions... 

>	RiemannSum(x^2, x=-2..4, method = left, output = plot, partition=[-2,0,1,1.5,2,2.5,3,4]);