e^(2x) Integration by Parts

e^(2x) Integration by Parts on the TI-89 Series

Raw Transcript

This is a video on integration by parts and doing a integral of e to the x. Some function with e to the x. Get started here, again 2nd alpha so that you can enter the letters of my code to get into my menu index 8( ). Closed parentheses tell the calculator that you want to do a program. You can scroll down to e^(x) integrate, that involves integration by parts. In this program you have In(x) , e^x, sin(x), cos (x) but choose e^(x).
Here is the formula: Evaluate a e^(x)
Integral
=v*u – ∫[v*(du)]dx
Here is an example: 2x*e^(-x) that you can add. So you would know how to put the function in or what function to use or something in that form. It will be on your test, and remember these come from tests so the test that I’ve seen I can do them, the program can do it. It is a certainly difficult subject if you ask me. I’ve programmed it for days and I couldn’t do a problem right now from memory without the help of my calculator. So any time you get a pause, you press enter and go to the next section. You press alpha x* press the blue key and e^ over the x button. You get this system of adding the e to the x like the calculator wants. Add x and closed parentheses. X*e^(x)
And here’s what you’ve entered: ∫[x*e^x]dx that’s for integration.
You can change it if you want otherwise select ok. This will come up
∫[x*e^x]dx
dv= (e^x)dx
v= ∫[e^x]dx
= e^x
u= x
du = (1)dx
You have to choose dv first as dv is the derivative. So we have to integrate that to get up to e. Then we have to get u and the derivative of u. There is a 1 in front of the u, so the derivative of u is 1. In case there was 3x, there would be a 3 there example, du = (3)dx.

Here’s the formula again, here’s what we tried to integrate
∫[x*e^x]dx
= v*u – ∫[v*(du)]dx
= (e^x) [x]
• ∫[(e^x) (1)]dx
= x*e^x
-∫[(e^x)]dx
So then we’re gonna evaluate and here’s the answer
∫[(x*e^x)]dx
= x*e^x
-e^x+c
Remember in tests you’re tested on curves and you get partial credit for anything, if you could put the formula down or anything intelligent you’re gonna get some credit for it. So that’s what my theory was when I was into tests and calculus and to somehow pass the class.
So enjoy my programs, everystepcalculus.com