here is my problem: find the upper and lower sums for the region bounded by the graph of [tex]f(x) = x^2[/tex] and the x-axis between x=0 and x=2. I understand what this problem is asking but i don't understand how to compte the left and right endpoints. the left endpoint is the following:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]m_{i}=0+(i-1)\frac{2}_{n}[/tex] = [tex]\frac{2(i-1)}_{n}[/tex]

and the right enpoint is given as this:

[tex]M_{i}=0+i\frac{2}_{n}[/tex] = [tex]\frac{2i}_{n}[/tex]

The lower sum ( left enpoint) is the following:

8\3 - 4\n + 4\3n^2

and the right endpoint is computed in a similar fashion.

my question is, how do i find the left and right enpoints? what is the formula for doing this? what if the lower bound is not zero but some other number, how would i find it then?

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Finding upper and lower sums of a region

Loading...

Similar Threads - Finding upper lower | Date |
---|---|

Finding an upper-estimate for a sequence. | Aug 9, 2014 |

Difficulty in finding upper limit of x | Apr 21, 2012 |

Find upper limit of improper integral - Numerical Integration | Feb 26, 2012 |

Help to find the upper bound | Aug 12, 2005 |

Finding least upper bounds | Apr 28, 2004 |

**Physics Forums - The Fusion of Science and Community**