U-Substitution Integration on the TI-89: Raw Transcript
This is a video on u substitution with regard to e to the x
a transcendental function and a little more difficult one
which I wanted to show you of how my programs react to that
to get started were going to press second alpha
put the i n d e x letters in this entry line of the calculator
and then press alpha and put in the eight and the
open and closed parenthesis press enter and you’re into my menu
you can scroll up or down to many things here it’s really integration by parts that your
always thinking about when you do a transcendental cosign sign natural log or
e to the x if you’re going to integrate them you’d go to think integration by parts first
but we’re going to scroll up to e to the x here
choose e to the x from that menu and we’re going to enter the function
you have to press alpha before you enter anything in the entry lines of my programs
so alpha and we’re going to do five times x times e to the three times x
squared I always show you what you’ve entered
so you can change it if you’ve made a mistake or something
and I always ask you whether this if this didn’t equal each other then it would
not be u substitution so you need to tell me that
by stating yes or no it does equal, x equals x so were going to
press yes and then I explain to you that anything inside
the parenthesis of e to the x
the derivative must match the outside and so here’s our original function
we re write it anytime you have a number or a
constant inside the integral you always bring it out and put it on the outside of
the integral before you start to integrate
which I’ve done here you take what’s left the x
and put it over here in the x dx so thats re writing it
and I choose the u for you. here is the derivative of three x squared
it’s six x and then you always take here’s another thing where
there is a constant or number is outside or next to the x dx
you always put that on the other side make du one sixth du equals x dx
transpose it by division and then you do everything
all this on your test or homework whatever exactly correct exactly as you see it
here we’re multiplying the outside of the integral
times the du of the one sixth comes of du comes out side too
gives us five sixrths and then you substitute three x squared for
u answer
five sixths times e to the 3 x^2 plus c pretty neat huh
every stem calculus dot com go to my site, buy my programs
and pass calculus
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