LRAM is a left hand approximation
delta x [f(a)+f(a+delta x) + .... f(b- delta x)]
RRAM is a right hand approximation
delta x [ f (a + delta x) + .... + f(b)]
MRAM
delta x [f(mid) + f (mid) + .... ]
Trapezoidal
delta x/ 2 [f (a) + 2f(a+delta x) + 2f (a+ 2 delta x) + ... f(b)]
To find delta x: b-a/n [a, b] with n subintervals
EXAMPLE: x^2-3 [1, 4] n=3
delta x = 4-1/3 = 1
LRAM: 1 [ f(1) + f(2) +f(3) ]
1[ -2 +1+6]
1[5] = 5
RRAM: 1 [ f(2) +f(3) + f(4)]
1[ 1 + 6 + 13] = 20
MRAM: 1 2 3 4
2+1/ 2 = 3/2
3+2/ 2 = 5/2
4+3/2 = 7/2
1[ f( 3/2) + f(5/2) + f(7/2)]
1[-3/4 + 13/4 + 37/4] = 47/4
Trapezoidal: 1/2[ f(1) + 2f(2) + 2f(3) + f(4)]
1/2 [ -2 + 2(1) + 2(6) + 13] = 25/2
I also learned this week that the answer to a derivative problem is never DNE..
I have not quite caught on to the other integration we learned (opposite of a derivative) especially the definite ones. I understand what we have to do and not to forget +c on the indefinite ones but it takes me a while to actually arrive at an answer. I guess this will just come with practice but if someone thinks they can help me catch on faster I would appreciate it.
practice practice practice :)
ReplyDeleteokay, with definite integration, you'll have a number as your answer, you don't have to add c at the end of it or anything. the problem will have a capital S looking thing with a number at the top, b, and a number at the bottom, a. So what you do is, integrate whatever they give you, then plug in the a and b that they give you into the integrated function. after that you just do the integral of b, minus the integral of a.
ReplyDeletei do more guess and check than anything..for example, i always think about it rather then just doing the "formula" way.
ReplyDeleteIf you think about it, then check your work, you should always get it right :)
hopefully.