:: Transcript ::

Hello tom from everystepcalculus.com we’re gonna do a calculus problem here is you see on the screen line integral this is an IJ and K. Once you see that this that’s what you’re going to do. It triggers you to for the menu to choose that okay anyways let’s do it index(8). I’ve already added the parameters and these variables into the into the simulator here so that it can save time when doing that index(8) to get to my main menu. We’re gonna scroll down here to the line integral or in the menu that’s at the alphabetical letter of L of course so we’ll scroll here down and then look for that. Here’s line integrals here we’re gonna press Enter and wait for when it says busy here it’s loading the program only does that the first time you loaded after that it’s very quick and we have IJ and K which is number 7 here you can scroll down like this or you can press the number 7 I like to press the numbers it gets there quicker and it loads the program for this type of problem. You’ll notice that the line integral this is the integral of the function for dr over the range of C and that equals (M)i+(N)j+(0)k here do you write all this on your paper exactly like it says here ok. We’re going to enter the function now normally you’d have to press alpha and then enter the minus 2x I here but I’ve already done that so and then before n2 asks you and before the O it asks you ok and it turns out to be here now here’s minus 2x I which is just like in the problem here plus y + 5 z k dr okay? You can change it if you want i say it’s okay. There’s line segments given no there’s no line segments given here is there okay so we’re gonna say no number 2 to his I J and K mentioned in the problem yes here’s here’s IJ and K here. RT there should be i’s this person didn’t put these in here right there should be i’s after each one I, J and K after these but yes and normally the problem will always have an IJ or K here so you add the I’ve already added them in here you can see it’s sine of T cosine of T i, J and K okay. I say it’s okay we’re gonna enter the range the range is given from zero to three times pi over two notice there’s no x in here this guy doesn’t know what he’s doing or girl whoever put this problem on the internet here and I’ve already added them so we’re going to go from 0 to 3 PI over 2. Say it’s okay. Now we parameterize the whole thing which we take x equals sine of T DX is the cosine of T y etcetera cosine of T dy is minus sine of T etc Z and DZ okay here’s the original integral minus 2 X 2 DX Y dy 5 times Z DZ the reason that dxdydz because we got to add that we’re gonna add that in the problem so we substitute all these into the problem here you notice here’s 2 times X there’s minus 2 times X and X is sine of T so then and then of course the DX is cosine of T and that’s the same thing for the other entrances here you’ll notice the quotation marks and your problem on your sheet you’d put you’d put parentheses around these quotation marks to indicate that you’re substituting it for x y&z; we clean it up here and condense it here’s what you get put this on your paper just as clean as that over the range of 0 and 3 times pi minus and divided by 2 we integrate okay here’s the integration you can do that in your head can’t you but I couldn’t I needed income calculator to do it here’s three times divided by two over that range so we’re adding the 3 PI over 2 to all the T’s in the problem the answer is 45 times PI squared over 8 at t equals zero we had zero for all the t’s in the problem and the answer is three-halves upper minus lower that’s always the way it is upper minus the lower and the answer is 54 you notice I’m pathetic line integrals are because you don’t even know what this is what is 54 mean what 54 square units 54 meters 54 feet what you know but calculus is stupid that way calculus is sudoko of math all right so anyways why would you do this in your brain or try to learn how to do this and memorize it for tests or anything else you can when you have a program like this you buy my programs for 40 bucks and 39 bucks I guess whatever it is and then you load them in your calculator and you can do a million of these including physics so make sure you think about physics too unless you want to just study this stuff for hours and hours and hours like I do I know a line integral is pretty good because I’ve been doing it for what two or three weeks now so now I know everything about line integrals and they’re all a waste of time in calculus but we need them to pass our homework and pass our tests okay you get out of that class move on with our lives so anyways go to my site buy my programs and enjoy passing a calculus okay have a good one

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