Lower Rectangle Method

[rsyed5]

Hi,
Can someone suggest a way to improve the lower rectangle method for area approximation...? I know one way is to increase the number of rectangles so if I put 100 instead of 5 rectangles i will get a better approximation. Any other way it could be improved...?
(please don't give other methods for area approximation, just the lower rectangle method)

 

[MathMathter]

What about adjusting the subinterval lengths so that they're shorter over intervals of greater change in the function? I've attached an example of that.

 

[Bob Brown MSEE]

Center the rectangle on the sampled point.

 

[rsyed5]

What about adjusting the subinterval lengths so that they're shorter over intervals of greater change in the function? I've attached an example of that.

Thanks, that's a good option.