Alright, so the main things we did this week were the limits test and integration. And I am quite happy because I did pretty good on my limits test, but integration on the other hand, I am not too sure about. The pictures that Mrs. Robinson drew for us about integration help explain what it is a lot better, but I cannot really do that on here, so I am just going to explain it in words and examples. As usual.
Integration uses Riemann sums, which is the approximation of area by using rectangles or trapezoids. Integration is just finding the area of something with a curve that you would not normally be able to get.
So there are four different methods of integration, LRAM, RRAM, MRAM, and trapezoidal.
The first formula you need to know is x=(b-a)/n [a,b] with n subintervals. You will need to know this because each of the next formulas require that you know what x is.
LRAM- left hand approximation. (this puts the rectangles used to find the area on the left side of the curve) x[f(a)+f(a+x)+...f(b)]
RRAM- right hand approximation. (this puts the rectangles used to find the area on the right side of the curve) x[f(a+x)+...f(b)]
MRAM- approximation from the middle. (this puts the rectangles right on top of the curve, so that the curve goes through the middle of each one) x[f(mid)+f(mid)+...]
Trapezoidal- this does not use squares, instead it uses trapezoids to eliminate most of the empty space inside the curve, and I think this is the most accurate. x/2[f(a)+2f(a+x)+2f(a+2x)+...f(b)]
The thing i'm having problems with is the stuff we learned friday, the indefinite and definite integration. The main thing is that I guess I haven't done enough problems to be able to do it easily, but I can do them when I look at my notes and at the example problems.
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indefinite and definite is almost the same
ReplyDeleteremember that you look at the exponent of what they give you and then add one...remember that the coeffient will be the reciprical of that...sooo
if you have to find the indefinite integration of x^2 it would be ... (1/3)x^3
the end
but if you have to find the definite integration between 0 and 4 of x^2 then you do the same thing, giving you (1/3)x^3, but you're not d0ne there, you have to plug in the zero and the four...so you get f(4)=(64/3) and f(0)=0 so you subtract the anser you get when you plug in the number at the top by the number you get from plugging in the bottom.
the end
hope it helps!
indefinite and definite is basically the same
ReplyDeleteremember that you look at the exponent of what they give you and then add one also remember that the coeffient will be the reciprical of that.
indefinite and definite integrals are easy after a lot of practice. for indefinite integrals, you will end up with an equation and you must mark it with PLUS C. or it will be counted wrong. for definite integrals you will end up with a number, this does not need plus c behind it. integrals are basically taking the derivative backwards. instead of subtracting one from exponents, you are adding one. and instead of multiplying the exponent by the coefficient, you are multiplying. it's the same for trig functions. if you are given cos(x), the indefinite integral of that would be sin(x) + c. it's pretty easy :-) definite integrals are just when you are given two numbers to find the integral of. it will have a long skinny "s" with a number at the top, b, and a number at the bottom, a. take the integral of both then plug in b and a. then subtract the integral of b minus the integral of a.
ReplyDeleteindefinite integration is super easy if you have X^2 you had one to ya exponet and divide by teh same number so you would end up w/ 1/X^3 which is the same as 1/3x^3 and definte you gonna have to numbers and you plug each one in then you subtract the answer you got using the bottom from teh top. and dont forget +c for definite and for indefinite you will get a number not an eqn
ReplyDeleteFor definite intergration its basically the same thing except after you intergrate you have to plug in the number at the top your S and at the bottom first you plug in the top and subtract by what you pluged in at the bottom and thatsyour awnser
ReplyDelete