Just Checking

[Lizzie]

The problem:
Suppose we wish to approximate the area under the curve y=f(x)=x² between x=1 and x=3, using 2 subintervals of equal width and either right of left endpoints for the rectangular approximation. What is the smallest value the approximation could have?

My answer:
5

Just wanted to check and make sure.

 

[stapel]

Well, which do they want, "smallest" or "subintervals of equal width"? Cuz we could go way small if we fiddle with the intervals....

Just looking at the graph, obviously left-hand endpoints are the way to go. So the intervals will have widths of 1 and heights of 1² = 1 and 2² = 4. The smallest total, under the given (no fun) conditions, is "5".

Eliz.

 

[Lizzie]

lol, that was the exact problem I was given, sorry if it isn't any fun. Although, I bet if you considered it fun, I would consider it the end to my Calc career, lol.