1/21/11

We're still doing the UNO study so i'll talk about what we've learned so far this week dealing with that. We've learned how to find area dealing with definite integrals. The definite integral of a function represents the area between the curve and x-axis. We also learned how to find LRAM, RRAM, TRAP, AND MRAM. All of these are similar to the same process, it's just following steps. To first start these problems it's best to draw the graph to give you a visual of how many shapes they have, and what sides are going to touch the x-axis. **With LRAM and RRAM you want to make sure you know which side(left or right) is touching the x-axis. Most of the time for LRAM when plugging in you're going to leave out 0, but with RRAM you're going to put 0 and leave out the last number. So after figuring out the graph, for LRAM and RRAM your going to take the bounds and subtract them, then divide it by the amount of rectangles. This will be your delta x. Then, your going to take the the amount of rectangles and plug them into the the equation. The answers you get will be used to find LRAM and RRAM, and to find area you will take the delta x, and multiply them by the answers you got when plugging into the equation (Don't forget to add all the equation answers together and multiply each one by delta x). Now to find TRAP you plug into the formula 1/2(LRAM+RRAM)<-**This is the short cut. To do it the long way, you have to plug into the original formula just like LRAM and RRAM, however to find the area follow the formula: 1/2(b1+b2)h. Lastly for MRAM you divide the rectangles that you draw on the graph to find the midpoint(point in between the two whole number parts). Plug the numbers you find into the original equation, and add them togetherxdelta x.

Here is an example of TRAM:

Use the Trapezoidal Rule to approximate (-x^2+4) dx, with the bounds x=0, x=3. How can you get a better answer?
*First things first, draw the picture out, which is going to be 3 trapezoids. We're going to plug in -0,-1,-2, and -3 into the original equation to get 4,3,0, and -5.
*Now plug into the formula 1/2(b1+b2)h, to get 5/2
**The answer would be 5/2