Well, this unit has been fairly interesting because of its relation with the previous unit. Now I can begin to see how everything in Calculus ties together. I have enjoyed this unit quite a bit because it has a decent amount of material that relates to Physics...
As well, it is fairly straight forward with the math, not a lot of outside the box thinking...
A key thing to remember is:
- There is more than one way to find the integral of a function
1. Using the formula: lim(n-->∞) [ f(x1)•∂x1 + f(x2)•∂x2 + ... f(xn)•∂xn ]
2. The Riesum Program in our Calculators:
LEFT: (left side of the interval)
RIGHT:(right side of the interval)
X CHOICE: (0=Left Estimate)
(0.5=Midpoint Estimate)
(1=Right Estimate)
N: (number of sub intervals)
3. "fnInt" function in our calculators: fnInt(Y1, X, min, max)
4. the function "∫ ƒ(x)∂x" in the 2nd Trace (Calc.) Menu
5. Calculate it Manually: LEFT ESTIMATE: Sum of all "ƒ(x)"s, minus the last "ƒ(x)" then multiplied by ∂x.
RIGHT ESTIMATE: Sum of all "ƒ(x)"s, minus the first "ƒ(x)" then multiplied by ∂x.
TRAPEZOID SUM 1: Sum of the first "ƒ(x)", the last "ƒ(x)", and (2 • all the "ƒ(x)"s in between) Then multiplied by ∂x. Finally divide by 2.
TRAPEZOID SUM 2: (LEFT ESTIMATE + RIGHT ESTIMATE) /2
Well, that's pretty much all for my BOB, good luck tomorrow... and:
KEEP PUSHING, and maybe, just maybe, that rock will stay at the top...
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