Year 12s: what will be the first way you research your future options? >>

C2 Trapezium rule overestimate or underestimate

Hi
I know the basic rule for easy examples of whether it is an under or over estimate... But in circumstances where some trapeziums go over the curve, and some go below (meaning it is a mix of over and under estimate), how exactly do you go about answering whether the overall estimation is an overestimation or an underestimation? So for example in a curve which is both convex and concave...

Reply 1

SamLLLLiu

This depends on the curve, if the curve is growing(the gradient is increasing), its going to be an overestimate. if the gradient is decreasing, then its an under estimate. you can figure this out by drawing actual trapeziums.

:smile:

Reply 2

Craig1998

Original post by MozFan99

Do you mean like a curve which has a positive gradient and a negative gradient?

I don't know how you'd suggest whether it's an overestimation or an underestimation. I don't really think they would ask you that unless you worked out the exact area first and compared the exact area with the area found using the trapezium rule.