here we go.
There were two types of integration. the first type was indefinite and the second was definite. you do the same thing for both except that for definite you see two numbers and at the end you have to plug them in and then subtract what you get by each other in order to get your answer. Remember that if it's indefinite then you have to put the plus 'c' but if it's definite then you just should have a number.
Then we learned about the change of variables which means that there is at least two different variables in the equation you are solving.
Then we learned about the area between the curves of graphs and the formula is bSa top equation minus the bottom equaion. in order to find a and b you need to set the equations equal to each other and then solve. what you solve for depends on what you're looking for or have in the equations. for instance if the area is on the y axis, then a and b need to be y values so the equations can be solved for x and opposite if the values need to be x values.
i kinda like the e integration the most. when you have the e integration, whatever it's raised to the e power will be your 'u' and 'du' will be the derivative of 'u'.
substitution
Okay, so I know the steps. They are extremely simple to understand; however, when I begin to actually do these steps I get thrown off by one thing: balancing. But anyway, here are the steps in my terms:
1. Identify your u (I identify this by looking inside the parentheses...and voila!)
2. Take the derivative of u to find your DU!!! (and don't forget the dx at the end)
3. Go back to original integration problem and substitute (ha! get it...substitution).
4. Then Integrate normal
5. Put all your u's back in to the original problem.
i dont remember the LRAM RRAM and MRAM. if someone wants to help me out w/ that
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First off, you have to know the formulas.
ReplyDeletemram:deltax[f(mid)+f(mid)..]
rram:deltax[f(a+deltax)..+f(b)]
lram:deltax[f(a)+f(deltax + a)...f(deltax + b)]
to find the delta x you use the formual (b-a)/the number of subintervals. after that you just follow the formula and then plug in to your original equation.
for riemann sums you have to know the formulas:
ReplyDeletemram:deltax[f(mid)+f(mid)..]
rram:deltax[f(a+deltax)..+f(b)]
lram:deltax[f(a)+f(deltax + a)...f(deltax + b)]
also you need to know how to find delta x..
deltax= (b-a)/# of subintervals.
Once you have that simply plug into the formula and you should be good.
A lot of times they're big fractions though which sucks.
For the RAM's, I suggest just memorizing the formulas and know that (b-a)/n = delta.
ReplyDeleteThen just plug in :):)
Also, MRAM confuses me when the numbers are totally strange....does anyone have a method of getting these?