C4 - Trapezium rule - is approx overestimating or underestimating?

Ah this is a simple question and would only gain you a one or two more marks but think I'm gonna need every mark I can get for C4!

When using trapezium rule to estimate area under a curve it sometimes follows with:

State with a reason, whether your approximation underestimates or overestimates the area of R.

Or similar. I really can't remember what the rule for this is. It's not always one of the other?

(btw this was from edexcel practice paper 4, but nowhere in the book so might not be on syllabus)

Thanks and goodluck tomorrow everyone.

Reply 1

silent ninja

You have to look at which way the graph curves. If its inwards (like an upside down quadratic), then the trapezium will underestimate. If you draw a curve then straight lines from one point of the cruve to another, you can see it misses the top bit off.

Similarly, one that curves outwards, like e^x, if you join points making trapezia under the curve, they overestimate as the straight lines from one point to the next go above the cruve.

Draw a quick little sketch and you'll see.

Reply 2

mike_J

well if its a curve like /-\ then its an under estimation, because there will be small amounts of the area under graph left untouched. if its such as \_/ then its over estimation. I believe thats correct.

Reply 3

Soph33

Cheers thankyou. That answered my question. Hate it when you miss the simple marks like that =]

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