Uploaded by Tommynnnnn on 02.09.2012

Transcript:

This video is going to be on integrals, rewriting an integral, and also evaluating one. Lets

get started – you have to press second alpha to put the letters of this code in – you

just do this once and up comes the menu for you – and you push alpha and then eight

and closed parenthesis, and then press enter, and up comes my menu of all the items – I

know that what I want to go to is the letter p, they go from numbers here, but then they

go p, so you can scroll down like this, all the way down – or if you know what your

after you can go alpha and then p, and I’ll go to – I want to rewrite the integrand

first – so I’m gonna – one of the most important parts – I tell you one of the

most important parts in here – and so you kinda go to this list here – and these are

the tough ones – so you go to your list and like for instance let’s do number six

here – press number six – n over x squared – you need to convert the denominator always

to a numerator, and that in algebra becomes x to the minus two, n times x to the minus

two, and then you integrate – you’re going to go integration of n to the x to the minus

two – which you can do it now, and here you have – n to – notice you add one to

the exponent up here and then all this you divide by that also – minus two plus one

– that equals n to the minus 1 – minus one. So that equals minus n over x – and

you can go to another one here, lets try number 5, here’s the cube root – well cube root

of course is exponent of, to the one third, and to integrate x to the one third, you have

to add one, well one in one third is three thirds, so you add that and divide, and put

that in the denominator also, and you have x to the four thirds over four thirds, and

when you divide by a fraction you invert and multiply, and so here’s the answer, three

x to the four thirds, over four. Ahh pretty neat huh, well I wanna do, I’m going to

go here and quit, lets scroll down here – and we can quit on either end of it – press

enter - now if you wanna, I’m gonna go alpha and p again to get back to the program, I’m

gonna – I want to evaluate, I’m gonna press number two, and evaluate – and for

demonstration let’s just do uhm – you have to press alpha before you enter anything

in this line here – alpha, and let’s go uhm – t times uhm – sometimes they use

the variable t – times – let’s use e to the x here, e to the x of three times,

t squared. And it shows you what you’ve entered here – I show you – and you can

go ok or change it – I’m going to say it’s ok, so – and I don’t do it step

by step particularly – uh – because this is u substitution – uhm – but anyways

– ah – this is the exact answer. And so that will help you immensely - ya know - checking

your integrals with any type of integral – quickly – and the step by step I have in other sections

of my programs like for instance u substitution – so – fabulous programs, check em out

at everystepcalculus dot com

get started – you have to press second alpha to put the letters of this code in – you

just do this once and up comes the menu for you – and you push alpha and then eight

and closed parenthesis, and then press enter, and up comes my menu of all the items – I

know that what I want to go to is the letter p, they go from numbers here, but then they

go p, so you can scroll down like this, all the way down – or if you know what your

after you can go alpha and then p, and I’ll go to – I want to rewrite the integrand

first – so I’m gonna – one of the most important parts – I tell you one of the

most important parts in here – and so you kinda go to this list here – and these are

the tough ones – so you go to your list and like for instance let’s do number six

here – press number six – n over x squared – you need to convert the denominator always

to a numerator, and that in algebra becomes x to the minus two, n times x to the minus

two, and then you integrate – you’re going to go integration of n to the x to the minus

two – which you can do it now, and here you have – n to – notice you add one to

the exponent up here and then all this you divide by that also – minus two plus one

– that equals n to the minus 1 – minus one. So that equals minus n over x – and

you can go to another one here, lets try number 5, here’s the cube root – well cube root

of course is exponent of, to the one third, and to integrate x to the one third, you have

to add one, well one in one third is three thirds, so you add that and divide, and put

that in the denominator also, and you have x to the four thirds over four thirds, and

when you divide by a fraction you invert and multiply, and so here’s the answer, three

x to the four thirds, over four. Ahh pretty neat huh, well I wanna do, I’m going to

go here and quit, lets scroll down here – and we can quit on either end of it – press

enter - now if you wanna, I’m gonna go alpha and p again to get back to the program, I’m

gonna – I want to evaluate, I’m gonna press number two, and evaluate – and for

demonstration let’s just do uhm – you have to press alpha before you enter anything

in this line here – alpha, and let’s go uhm – t times uhm – sometimes they use

the variable t – times – let’s use e to the x here, e to the x of three times,

t squared. And it shows you what you’ve entered here – I show you – and you can

go ok or change it – I’m going to say it’s ok, so – and I don’t do it step

by step particularly – uh – because this is u substitution – uhm – but anyways

– ah – this is the exact answer. And so that will help you immensely - ya know - checking

your integrals with any type of integral – quickly – and the step by step I have in other sections

of my programs like for instance u substitution – so – fabulous programs, check em out

at everystepcalculus dot com