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

Trapezium rule help!

If the trapezium rule is used to measure the integral of f(x)dx between 1 and 0 on the x axis, by splitting the interval 0<= x <= 1, into 10 intervals then an overestimate of the integral is produced. So why does the trapezium rule of 10 intervals underestimate the integral (between 1 and 0) (1-f(x))dx

I know that increase of 1 on the y-axis changes nothing regard to areas, but why does the reflection in the x axis change it from an overestimate to an underestimate? ... some clarity to my confusion would be greatly appreciated! Thanks

Reply 1

lazy_fish

Original post by Pliskin

...

Consider the two curve types with which the Trapezium rule provide an underestimate and overestimate to. What happens to a curve of one type if it were to be reflected in the x-axis?

Hope this helps. :smile: