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