PROGRAM:LeftNI
:A+Y1*H
A:X+H
X:Disp X,A
General method: Formulate the problem as finding the area between the graph of the function, f, and the x-axis from x=a to x=b. (Area below the x-axis is counted as negative.) Subdivide the interval [a, b] into n subintervals of equal width. This width will be h=(b-a)/n. The areas of rectangles with these subintervals as bases and heights equal to the curve's height at the left endpoint of the subinterval are computed and summed up as the process moves from a to b.
Program:
PROGRAM:LeftNI
:A+Y1*HA
:X+HX
:Disp X,A
To use this program, place the formula for f(x) as Y1 in the "Y=" menu. Place the value of a in X, the value of h in H, and 0 in A. Execute the program n times. Since the value of X displayed in each step is the right-hand endpoint of the subinterval, the user can simply monitor this value rather than counting from 1 to n.
Notes: The same idea can also be used replacing left-hand endpoints with right-hand endpoints or midpoints of the subintervals. The student should build programs RightNI and MidNI which implement these ideas. (Hint: RightNI can be constructed by interchanging two lines of LeftNI.)
