Use the Fundamental Theorem of line integral to evaluate the integral (y^2-3*x^2)dx + (2*x*y+2)dy

:: Transcript ::

Hello Tom from EveryStepCalculus.com a

problem in calculus regarding line

integrals one of the most pathetic

sections of calculus completely worthless

just really puzzles all calculus is is

puzzles like sudoku puzzles

and some professor will say that it’s

important for something else and I’ve

never found that after 25 years. So

anyways let’s do this so you can pass

your test here’s a question that

some kid put in and I’m going to show

you how that works and my programs. index(8) to get to my menu I’m going to scroll

down here to line integrals that’s these

subject matter here’s the line integrals here

and we’re going to go number six here

dxdy because that’s what they’re asking

here D with DX and dy okay so then we’re

gonna choose that in the menu number six

I press the number or scroll to it I’ve

already entered the functions in here to

save time with the simulator here so

here’s what the function is the integral

DX dy you’d put that in yourself

pressing alpha first and then you

I have a choice of sitting it’s okay or

you could change it in case you made a

mistake but you’re gonna enter that

yourself by pressing alpha first

remember that E and there’s line

segments given yes they are and they’re

X Y and X 2 y 2 because they give you x

and y and then X 2 y 2 I say okay

and I put these in already one and minus one zero looks pretty good we’re going to say okay to that

parameterize it, change it with t-values and here’s the

form of the trick for that remember this

this is the big trick took me

quite awhile to figure this out from the

way professors teach things

they skip the easy stuff which is tough

for maybe you or me

and we do the y-value that’s what it is

anytime you’re parameterizing

a function the range becomes zero to one

okay remember that so now we have the X

and now we’re gonna do the derivative of

that which is minus three here’s the y

value that we got and we’re gonna do the

derivative of that which is minus one

original integral is this okay now we’re

going to substitute all this in here

putting the one in just like you says I

have quotation marks here which this

simulator does but you’re gonna put your

gonna put parentheses around this on

your paper okay because remember they

want to explain a step it’s that when

you get points for each step you do

and so you’re gonna add all these

anytime you see quotation marks you’re

gonna put a left or right parenthesis

okay to clean it up and then we

do the actual math of that which is this

okay three we’re gonna integrate it

of course you could do that without this

help right no problem just

anybody can do integral is really easy I

don’t think so and we’re gonna at T

equals one which is the upper limit

we’re going to enter the one for all of

all the steps etc and we’re gonna enter the zero at T

equals zero we’re gonna enter the zero

for all the exes okay that equals zero

the other one was five so take the upper

limit minus the lower limit five minus

zero and here’s the answer five units

okay now we don’t even know what units

are I mean what are we doing with line

intervals let’s see we’re finding the

distance or something around this thing

is so Pythagorean theorem anyways so but

what do we care we just need to pass the

test so go to my site buy my program

they’re only forty dollars you get three

hundred and over three hundred and

seventy programs in your calculator to

answer most of test problems in calculus

and you’re going to get six or seven or

eight right versus the person sitting

next to you and that’s all you need

because of the class curve to pass that

class or maybe get even an A so think

about that okay the price is pretty

cheap compared to what you’re paying for

college nowadays so think about that go

to my site, buy my programs, and pass

calculus hey have a good one