Blog #22

Well, yet another blog. This week, we continued the UNO study and learned more about the LRAM, RRAM, MRAM, and TRAM. For this blog, I’m going to go over how to find LRAM and RRAM.

These methods are used to approximate the area of the region bounded by a curve and the x-axis.
LRAM is the left Reimann Sums. It uses the left points touching the graph.
RRAM is the right Reimann Sums. It uses the right points touching the graph.
In order to get an accurate estimation, you need to do both LRAM and RRAM because one will always be an underestimate and one will always be an overestimate.
Reimann Sums is the method of breaking up the region into smaller, easier shapes and adding the area of each one together. It is commonly used with rectangles.
First, the area of a rectangle is length times width. So, we must find the length and the width of each rectangle, then add all of them together.

Ex. Find the area of the region bounded by the curve f(x) = x² and the x-axis between x=0 and x=3. Use 3 rectangles.
First of all, x=0 and x=3 are your bounds. So to rewrite this equation, it would be: 3S0 x² dx. (*”S” is the integral symbol.)
Next, what is the width? To find it, subtract your upper and lower bounds, then divide by the number of rectangles: (3-0)/3 = 1
Now, to find the lengths, plug in to the original equation every number between 0 and 3 that is 1 width away. The numbers will be 0, 1, 2, and 3. To plug in: (0)² = 0; (1)² = 1; (2)² = 4; (3)² = 9
Finally, for LRAM, multiply the width by the first three lengths (all of the left points) and add them together: (1)(0) + (1)(1) + (1)(4) = 5
For RRAM, multiply the width by the last three lengths (all of the right points) and add them together: (1)(1) + (1)(4) + (1)(9) = 14
Your answer: 5 < area < 14