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middlesum

  

numerical approximation to an integral

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

middlesum(f(x), x=a..b)

middlesum(f(x), x=a..b, n)

Parameters

f(x)

-

algebraic expression in x

x

-

variable of integration

a

-

lower bound for the range of integration

b

-

upper bound for the range of integration

n

-

(optional) indicates the number of rectangles to use

Description

• 

Important: The student package has been deprecated. Use the superseding command Student[Calculus1][RiemannSum] instead.

• 

The function middlesum computes a numerical approximation to a definite integral using rectangles. The height of each rectangle (box) is determined by the value of the function at the midpoint of each interval.

• 

Four equal-sized intervals are used by default.

• 

The command with(student,middlesum) allows the use of the abbreviated form of this command.

Examples

Important: The student package has been deprecated. Use the superseding command Student[Calculus1][RiemannSum] instead.

withstudent:

middlesumxklnx,x=1..3

12i=0354+12ikln54+12i

(1)

middlesumsinxx+sinx,x=1..3,12

16i=011sin1312+16i1312+16i+sin1312+16i

(2)

See Also

Student

student(deprecated)[leftbox]

student(deprecated)[leftsum]

student(deprecated)[middlebox]

student(deprecated)[rightbox]

student(deprecated)[rightsum]

student(deprecated)[simpson]

student(deprecated)[trapezoid]

Student[Calculus1][MidpointRiemannSum]

Student[Calculus1][RiemannSum]

value

 


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