Finding the Area Under Curves + Summation.

First off, hello to everyone! I was recommended from other forum to this one in order to get math help. So let's see how this goes. Right now, I am having a lot of issues with trying to find the area underneath a curve, a lot of concepts just fly over my head, it seems. As far as summation goes, since the two are thrown together, I just have issues finding the patterns, if that makes sense. But, let me post an example problem and I hope that with some help I can understand this better. Let's do some math! (Nerd)

**Use the left and right endpoints and the given number of the rectangles to find two approximations of the area of the region between the graph of the function and the x-axis over the given interval.**

*g(x) = x*^{2} + 1, [1,3], 8 rectangles

Re: Finding the Area Under Curves + Summation.

Hey CrimsonDreams.

Hint: Divide your region [1,3] into equally spaced sub-intervals (example with 0.1 difference you get [1,1.1,1.2,....]) and then use two different numerical techniques.

A suggestion for the two techniques include the mid-point rule and the trapezoidal rule.

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Re: Finding the Area Under Curves + Summation.

Hi,

Pictures are often very helpful. Here's a diagram for the approximation using left hand endpoints:

Attachment 27677