This break flew by as usual. But seniors the year's about to fly by! :) So, i thought i was going to remember this after the break, wow i thought wrong. I'm gonna post fourteen and fifteen together since the holidays overwhelmed me and i completely forgot last week. Let's get this going.
Integration is what we've learned lately. The first thing we talked about was Riemann Sums. It is the approximation of area using rectangles oor trapezoids. I did okay with these when we first learned them but now i'm kind of clueless. I can put together how to do LRAM and RRAM but get completely lost with MRAM and TRAM if anyone would like to further explain these to me. I have to formulas it's just hard for me to follow exactly what to do by looking at them..
Now on to Integration itself. Remember integration is the opposite of a derivative. We never use the rules of derivatives inside integration so don't try to do product and quotient rule! The problem will always be manipulated to be integrated. I've finally got down definite and indefinite integration of polynomials, so I'll do one of those as my example problem:
S x^2 + 4x + 9 dx
= 1/3x^3 + 4/2x^2 + 9x + C
= 1/3x^3 + 2x^2 + 9x + C
simple enough, right? It's like working backwards. Just don't forget the plus C in all indefinite integrals!
Definite integrals are also pretty simple. You are given an interval to integrate with. All you do is integrate regularly and then after plug in the numbers you are given. The answer is always a number, f(b) - f(a).
As for the things i need help with, which are a lot may i add..
Substitution- just in general, i need serious guidance
Riemann sums- more or less MRAM and TRAM
change of variables- i caught on well to this in class, i think i just need a reminder
e and ln integration
Now a specific question i have is a problem like
S -4x^-3 - 5x^2 + 5x^-1dx
i was integrating it normally but i got confused at the last part.
adding 1 to -1 gives you 0 and i didn't know what to do.
I think this is when you do natural log integration but i can't remember exactly, so if anyone can answer this for me I'd love you forever :)
Well i need to go finish working on this MONSTER packet. If anyone is up for helping me catch on a little better my number is (504) 919-7250. See yall tomorrow!
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MRAM: The formula is delta x[f(mid) + f(mid) + ... ]
ReplyDeleteAll you have to do is find delta x by subtracting b-a and then dividing by n and then finding your midpoints using the same numbers as you used for LRAM then plug your midpoints into the formula and solve.
EXAMPLE: f(x) = x-2 on [0,4] with four subintervals.
so delta x= 4-0/4 = 1
your numbers would be 0, 1, 2, 3, 4
Find the midpoint between each:
0+1 / 2 = 1/2
1+2/ 2 = 3/2
2+3/2 = 5/2
3+4/2 = 7/2
and then you plug in
1[f(1/2) + f(3/2) + f(5/2) + f(7/2)] and solve.
Trapezoidal is basically the same steps except instead of multplying by delta x, you multiply by delta x/2 and the formula is
delta x/2 [f(a) + 2f(a+ delta x) + 2f (a + 2dletax) + ... f(b)]
So using the same problem:
1/2[f(0) + 2f(1) + 2f(2) +2f(3) + f(4)] and then solve.
For the problem with 1+-1, it is natural log so 5 ln |x|.