Trapezoidal Rule calculator App for TI-89 Titanium
Good morning friends from San Diego, everystepcalculus.com everystepphysics.com This is Tom I’m gonna help you with this trapezoidal rule now, this is another Sudoku problem from calculus. The math subject that answers nothing useful.
We’re gonna do this, I’m gonna do the whole thing for you and show you how my programs are so fabulous for this kind of stuff. Otherwise you can study it for hours and never know what we really need to do. Like for instance how does this help you here you know?
I mean so you’re gonna put down, all these people, this is a yahoo problem you know? And this kid wanted to know, he had four question marks after it saying, oh my god I’m panicked, what do I even start, what do I do with this stuff you know?
There’s no system to it in other words, you really don’t know what you’re doing. There’s a formula for the whole thing if you of course find it out and I have to use that for my programs to program my calculator.
But anyways we’re gonna do this one here let’s do it. Let’s go to the main menu here. And we go to the main menu and we’re gonna go up with the cursor because I want to go to the trapezoidal problem. So we’re gonna go to the T section which is closer to the bottom of the alphabet here. So we’re going to go up here to t r a. Here it is here. Press Enter. And we’re gonna enter our function.
“s” they use s, have no idea why. A lot of books a lot of professors use s here for the area. This is the area. Which every integral is is a finding the area under a smooth curve, it better be smooth, and then you better have a limit, limits of integration which is here a and B okay?
So you’re always finding, with an integral, you’re always finding the area under a curve. Or if they use certain formulas you can find spheres, or you can find, not areas but… What am I trying to say, volumes okay? Sorry my mind went blank therefore for instance, for a second.
So anyways here’s what you’re trying to find. You’re trying to prove that you’re the same thing that a definite integral will do in calculus okay? So we’re going to enter the function here which is pathetic x squared. Notice that all these functions are really simple because that’s all there is is simple functions you know?
Alpha X squared. Say okay. We’re going to enter the range from alpha zero. They give you to alpha -2 okay? Yep, enter intervals intervals two four four of them alpha 4. And here’s the formula trapezoidal rule formula. Ok? Change of X divided by two times F of a, a is the lower limit plus 2 times f of X 1 plus 2 times f of X 2, 2 times X 3 X 4 etc.
And then you can go all the way up to whenever how much you want. I only do 10 10 units here with my programs you can do whatever you want. But I think, and you put F and B in there and put those in there in that 2 and B is the upper limit. Let’s not talk about this baloney too much.
Change of X we do that which is B minus a divided by n, it turns out to be 1/2 great. I got that . We’re going to compute the intervals . Okay? So X at 0 equals a equals 0 the lower limit is 0 so that goes here. x1 equals 0 plus 1/2 change of X times 1 equals 1/2.
X 2 equals 0 plus 1/2 times 2 equals 1 etc. Notice how many you go up to this is a system. Now you can remember this ok? So even if you, my programs, because I’ve I’ve programmed it. I find the system the best system for this crap and give it to you so that even if you don’t want to use the calculator in a test or something you can at least try to remember something.
Let’s see you know x3 okay we’re going to put 0 which is a lower limit plus 1/2 which is N. Or the change of x times third one which is x3 equals 3 halves. Okay? Etc. We got four of them so we’re done. We’re gonna place those into a function. f of X x1 equals F of 1/2 so we put 1/2 in the function compute it 1/4 etc.
Put 1 into the function computed equals 1. Three halves into it nine fourths 2 into it for 4 so X is 4 is 4 ok? Here’s the definite integral again which is the only sane integral there is. Indefinite integral which is just always a plus C after it 10 million plus C’s constants that you’re supposed to add to the integral after you compute it. And you know how do you find the extra constant you know in things. I don’t know.
So now we’re going to do the formula for the approximation which is change of X divided by 2 times F of a etc. for 4 of these one two three four. At the end notice that F of B and we put them in here. We’re going to multiply this which is you know the 1/2 divided by 2 which is the new change of X here.
And these are all computed as we write everything you see on your paper okay? Keep going the answer is 11 fourths 2.75 square units. when you add them all together and multiply times they have 1/4 so that’s what he got here this answer person. Not close to the real answer of 2.67 so let’s go back and let’s go to the main menu. Let’s scroll down here to definite integral that’s what you’re asked for in the and of course I do definite integral’s all the way up to X Y Z here’s just to the x1 so we’re going to choose that one just when you got an X in the function .
We’re gonna enter the function alpha X squared okay? I’ll show you what you’ve answered I’ll show you what should enter so you can change it in case you made a mistake. I said it’s okay. We’re gonna enter the range alpha zero. And alpha-2. Looks good we’re gonna integrate it just X cube divided by 3 that’s the integration of the x squared. At x equals two and the function turns out to be 8/3 at x equals zero equals zero upper minus lower 1/3 minus 0 equals answer 8/3 equals two point six seven square units.
He’s put down to point six seven I like to I like to rub it in that you’ve actually found the area of something okay is if that’s so GD important in life. You know telling you calculus should only be taught to math majors let them deal with it not us. We’re the sane people don’t go crazy.
Anyways go to my site think about it. One thing I want you to do if you can if you get this far is it go over the right corner there and subscribe I need subscribers I got to get to a thousand subscribers so I can change and edit my videos okay? So maybe you can help me in that okay? And otherwise go to my site buy my programs calculus 1, calculus 2 or 3, or calculus 1,2,3.
And you know all this is in the menu like the back of a fabulous calculus book and you’ll have it for the rest of your life take your calculus book and throw it burn it in two minutes after you buy my programs. Never seen, you never use it again but anyways you have a good one, and I’ll help you all you can I mean you you can you can email me and I’ll help.
Send me your tests and I’ll show you how they work I’ll show you what you’ve answered in this tests and you’ll never you’ll never fail at another calculus test for the rest of your life if you buy my programs. Never okay? And I could never pass a calculus test without my programs and I’ve done it for twenty five years studied this stuff. All right you have a good one. Good luck on your calculus!