This week we reviewed limits and took a test on them on Wednesday.... after reviewing limits, we then learned how to do integration. The first part of integration that we learned was:
LRAM- this is when they want left hand approximation
x[f(a)+ f(a+x)...f(b-x0)]
RRAM- when you want right hand approximation
x[f(a+x)+...+f(b)]
MRAM- this is when you use the midpoint formula
x[f(mid) + f(mid)+...]
Trapezoidle- the best graph approximation will always be trapezoidal
x/2[f(a)+2f(a+x)+2f(a+2x)+...f(b)]
These formulas are primarily used when finding the area under a curve.
The next concept we learned was definite and indefinite integration.
When working indefinite integrals, your answer will always be an equation.
When working backwards always remember the formula to find what the derivative was:
sx^n= x^n-1/n+1... and always remember to add a +C at the end to account for any number that may be there.
Definite integrals will always give you a number for your answer. Denfinite integrals are used to sometimes find the area. the formula is bSa f(x)dx=F(b)-F(a)=#
One of the things i do not understand about integration is the absolute value problem that was worked on the board. If anyone can help me out i would appreciate it. Some of the other things i am still not good at and having trouble with are angle of elevation, and linearization.
Oh and for those of you who are still having problems with related rates, here is a quick reminder:
1. Identify all variables
2. Identify equations that will be used
3. Take the derivative of the formula
4. Plug in all numbers
5. Solve for the unknown
Hope this helps!
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for the absolute value one...i dont have it in front of me
ReplyDeletebut i know that you do almost the same stuff just with extra steps.
for instance whatever you have in the absolute value, you need to set it to zero and then you take whatever you get from that and put it between the numbers on the top and bottom of the integration sign.
next take the first split integration and put a negative and then the equation [or whatever you have] in the absolute value in parenthesis. after that you can distribute the negative in. next you have the other part that was split up and so you just put the stuff you put into the first one, just not the negative. after that you just do the integration part of it with the two numbers that you have on the top and bottom of the sign like you do for the definite problems. then take the two and add the answers you get from doing that to both of them together and then that's your answer!
HOPE IT HELPS!