holidays!!!!!! are over and reality is unfortunaltly back so.....here we go again with the almighty calculus blog and yes i am doing on monday because i forgot....
LRAM is left hand approximation and the formula is:
delta x [f(a) + f( delta x +a) .... + f( delta x - b)]
Say you are asked to calculate the left Riemann Sum for -4x -5 on the interval [-3, -1] divided into 2 subintervals.
delta x would equal: -1+3 /2 = 2/2 = 1
1[ f(-3) + f(-3 +1)]
1[ f( -3) + f(-2)]
then plug into your equation
RRAM is right hand approximation and the formula is:
delta x [ f(a + delta x) + .... + f(b)]
so using the same example:
1[ f( -2) + f(-1)] and then plug into your equation
MRAM is to calculate the middle and the formula is:
delta x [ f(mid) + f(mid) + .... ]
To find midpoints, you would add the two numbers together then divide by two
In this problem the numbers would be: -3 , -2, -1
-3 + -2/ 2 = -5/2 and -2 + -1 / 2 = -3/2
so 1[f(-5/2) + f(-3/2)] and the plug in
Trapezoidal is different because instead of multiplying by delta x, you multiply by delta x/2 and you also have on more term then your number of subintervals.
The formula is : delta x/2 [f(a) + 2f(a + delta x) + 2f(a+ 2 delta x) + ....f(b)]
For this problem: 1/2 [ f(-3) + 2 f(-2) + f( -1)] and then plug in.
Substitution takes the place of the derivative rules for problems such as product rule and quotient rule. The steps to substitution are:
1. Find a derivative inside the interval
2. set u = the non-derivative
3. take the derivative of u
4. substitute back in
e integration:
whatever is raised to the e power will be your u and du will be the derivative of u. For example:
e^2x-1dx
u=2x-1 du=2
rewrite the function as:
1/2{ e^u du, therefore
1/2e^2x-1+C will be the final answer.
related rates:
The steps for related rates are….
1. Pick out all variables
2. Pick out all equations
3. Pick out what you are looking for
4. Sketch a graph and label
5. Create an equation with your variables
6. Take the derivative respecting time
7. Substitute back into the derivative
8. Solve
limits:
Rules for Limits:…
1. if the degree of top equals the degree of bottom, the answer is the top coefficient over bottom coefficient
2. if top degree is bigger than bottom degree, the answer is positive or negative infinity
2. if top degree is less than bottom degree, the answer is 0
so I am still not understanding e integration and even though I have an example up im still having problem working them.
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e integration isn't too hard to grasp once you realize what's going on. For e integration, you will always wind up with e^u again in your original problem. Recall that the derivative of e^u is e^u times derivative of u. So really all you do with e integration is make sure the entire derivative is there...and if it isn't you need to modify so it cancels it out. For example
ReplyDelete(4x-1)e^(2x^2-x)
Really you set your u to what the e is raised to
So u=2x^2-x so du = 4x-1
Now substitute in
e^u times du
The integral of e^u is just
e^u. That's all you need!
For e integration, just remember you u will always be what e is raised to. your du will be the derivative of you. If you find that there is something extra in your du that is not in the fucntion, manipulate the function to show that you added it. In the end, your integral will be e^u. Hope this helps girl!
ReplyDeletealkfdjg
ReplyDeleteyou make sure your u is what e is raised to. your du is goonna be the der of u and if there is something extra like a 2 you'll add a 1/2 to it. its simple
ReplyDeleteE integration is a little tricky, but just remember that what the e is raised to will be your u and if you have the du in the problem then you're good, but if you don't then you'll have to add the recprical of it on the outside and it on the inside to make sure that you have it equal.
ReplyDeleteE integration is really easy. It's actually easier than integration without e. The exponent e is raised to will always be you. Take the derivitive of that and make it du. If du is in your problem, you have nothing to add outside. If something is missing from du, put it on the outside of your problem
ReplyDeleteEx: if you're missing a 2
1/2 S udu
1/2[1/2(u)^2 + c]