Thread: Any one help Upper and Lower sums

Can someone show me how to find upper and lower sums and hence solve definite integral of x^3 for [0,2]

thanks

Originally Posted by jamtheman

Can someone show me how to find upper and lower sums and hence solve definite integral of x^3 for [0,2]

thanks

Do your class notes or textbook contain no reference material? Try reading this: http://www.geometer.org/mathcircles/riemannint.pdf

Use the example as a model for integrating x^3 over [0, 2]. If you're still stuck, please show what you've tried and where you get stuck.

Well ive found the upper sum easily enough to be (2/n)^4 * [{n(n+1)}/2]^2
and i wonder could you derive the lower sum simply by knowing the difference and subtracting from the upper sum?

Originally Posted by jamtheman

Well ive found the upper sum easily enough to be (2/n)^4 * [{n(n+1)}/2]^2
and i wonder could you derive the lower sum simply by knowing the difference and subtracting from the upper sum?

No. I would guess that you have derive the lower sum along the same lines that you derived the upper sum. Then take the limit as n --> oo of either one of them.

By the way, when asking a question you should post what you've been able to do so that people don't spend their time posting things that you already know.