WEll this weekend is bad i basically played in the wet freezing cold rain for some reason that is unkown to mankind all exsitiance of life and the results were oustanding Friday i felt bad Saturday i felt worst Sunday i felt horrible and i don't think im going to school tomorrow(monday). I BELIEVE I HAVE THE FLU AHHHHHHHHHHHHH!!!!. This week we basically just messed with those clickers all week and me i grabbed the wrong number because i did not pay attention to the numbers and i still don't know my number so i might grab yours next be afraid very afraid.
This week in Calc we were still on integration we learned washers and disk
The formula for the volume of disks is (top)^2-(bottom)^2 dx
The formula for washers is S(top)-(bottom)
The steps are:
1.Draw the graphs of the equations
2. subtract the top graph's equation by the bottom graph's equation
3. Set equations equal and solve for x to find bounds
4. Plug in the bounds and the outcome of step 2
5. integrate
I understand washers and disk which is great but theirs still a bunch of things in integration i don't understand
1. I still have trouble wiht Trapazoid
2. I don't really know when to integrate and start working on the problem
3 EVERYTHING WE LEARNED
Those are my 3 biggest problems so can anyone help me wiht 1 and 2 but i thinkg that 3 is to broad of a topic for anyone to help me with.
AS always thanks.
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I'm assuming that by trapezoid you me trapezoidal so I'll explain that.
ReplyDeleteFor trapezoidal, you plug into the formula
delta x/2 [f(a)+ 2f(a + delta x) + 2f (a+2 delta x) + .... f(b)]
To find delta x your formula is b-a / n
EXAMPLE: x^2 + 2 on [1, 4] with 3 subintervals
delta x would be 4-1/3 = 1
then just plug in: 1[f(1) + 2f(2) + 2f(3) + f(4)]
and solve: 1[3+ 12+ 22+18] = 55
Integration is just the opposite of a derivative. There is indefinite and definite integration
Indefinite: Same rules as derivatives except you are working backwards
Polynomials: instead of subtracting one from exponent, add one
x^2+4x+9 dx
1/3x^3 + 2x^2 + 9x + c
Don't forget the plus c
You can always check your answer by take the derivative of it
Definite: Works the same way except you are giving an interval that you have to plug in. f(b) - f(a)
x^2 dx on [0,3]
integrate: 1/3x^3 then plug in
1/3 (3)^3 - 1/3(0)^3
9-0 = 9
Note: you will always get a number for definite integration
Trapezoid is probably the most acurate way to find area under a curve
ReplyDeleteThe formula is:
x/2[f(a)+ 2f(a+x) + 2f(a+2x) + ... f(b)]
So, to explain this, you're basically going to start off with a and end up with b. In LRAM, RRAM, and MRAM you multiply everything by x, but for trapezoid remember to multiply everything by x/2. Some people think because you're multiplying everything by x/2 you should add by it on the inside as well. You shouldn't do this, just add by x.