Hello. Tom from everystepcalculus.com and everystepphysics.com. Another Green’s theorem regarding a unit circle and its dividend. Index 8 get to my menu scroll down to Green’s theorem year what is the only reason that we’re studying this stuff is crap is to pass our calculus test passed her test that’s the only reason we have no interest in it whatsoever unit or going to work at NASA we have no interest in it keep that in mind raising our professors charity she disliked there are some basis for some goodness 40 are evergreen serum here problem from Yahoo gets have to press alpha beforehand or anything in these entry lines here is now four times why where the axe function and three times C looks pretty good reason to I say it’s ok they gave me MRP using MNE and here and it goes as the partials hebrew 3-6 unit circle convert to pull their situations circles Mexico said it takes our way it was caught sight of theater times are and we’re gonna do the first or detain Dr agreed defeated come up with minus six times over 250 compute that come up with minus 12 hi I mean agreed that Dr in a girl putting minor stroke pioneer over 10 subtract them and we come up with minus 12 high school career. Pretty neat, huh? everystepcalculus.com and everystephysics.com. Don’t do this step without my programs. Have a good one.
Hello. Tom from everystepcalculus.com and everystepphysics. com. Another example of Green’s theorem and show you how that pathetic. Index 8 lyrics to get to my menu. Scroll down to Green’s theorem. Generally in a test, they give you, your’re supposed to use Green’s Theorem or something like that. So we choose Green’s Theorem. And we enter our x and y or i and j functions. This one is You have to press alpha before you enter anything in my entry lines here on the calculator ok? Alpha plus three times x squared plus y. three times for the j or y value. Three times x press alpha. Alpha three times x times y squared. Imagine the knucklehead professor that’s still refer to which taking up these functions here that would work. That’s what they are asking for you to do. Just find the area of a triangle. Which is of base times height. I give you a chance to change it. The m or the p function is 3 x squared plus y and the q or the n function is three x y squared. It uses different letters for which professor you’re talking to or which book you use. And the partial of m, i use m here. The partial of m with the partial of y is one and the partial of n with the partial of x is 3y squared. And we subtract those going to the formula. That’s 3 times y squared minus 1. And we’re going to choose, I’m going to go up and press the up cursor to go to the bottom of the menu to get to triangle. This is a Yahoo problem. Right triangle, okay? What do they give you? They either give you 3 points or the give you this y equals, y equals, x equals. This case, it’s the first one there. Choose that. Then I’m going to go alpha zero, it chooses the boundary if you’ve ever worked with Green’s Theorem, that’s the most difficult thing is to figure out what the boundaries are. And that’s 2nd alpha, alpha x 3rd one is the x value is alpha 1. I say it’s ok. And we do the green set up. This is what we found here. For the partials these regions d y dx.
So we integrate dy.And then we over the range that was given which is a x is 0. Comes out to be x cubed minus x. And then we integrate dx. x cubed minus x with respect to x over the range of 1 0. So the answer is minus one quarter squared units. Pretty neat huh? everystepcalculus and everystepphysics.com. Don’t try to pass Calculus without my programs. Believe me, it’s much easier. Have a good one.
Hello everyone, Tom from everystepcalculus.com and everystepphysics.com. You can buy my programs to pass your physics and calculus classes step by step on all the problems which you need to show your work. Index 8 to get to my menu. We’re gonna do the Green’s Theorem, today, in this one. And they give us a triangle with vertices to figure out the double integral. So we’re going to choose index 8 to get to my menu and we’re going to scroll down here to Green’s Theorem it’s alphabetical. There’s Green’s theorem there. They give us the x or the i function from the line integral. You have to press Alpha before you enter anything in these entry here. Alpha x squared times y squared. And then we’re going to choose for the y the J function. Alpha 4 times x times y cubed. I always show you what you’ve entered. Here is the line integral, it really should really be called the curved integral. There are no integrals on lines. Straight things, everything needs in exponent to work. That’s the reason they use cosine and sine so much because it’s a sine wave which is a perfectly smooth curve and the use balls and spheres and etc, to do all their calculations, calculations as I see it. Calculus solves nothing in real life does nothing for anybody. Just a Soduko of math. Something that people do to waste time just like crossword puzzles in English. So anyways there’s a line integral of it and I’m going to say it’s ok to go with. P and q system or m and n system. I use the the n and m, depending on which professor you’re dealing with or the book. Compute the partials, partial of m with a partial of y is this. Partial of n with a partial of x divided by the partial of x is this . And we’re going to subtract the m from the n partials. And this right here. Ok and so now, we’re going the triangle, which they give us. We are going to choose a number to the points. They don’t give us y y x, they give us 3 points. First point is 0 0 , second point is 1 and 3, we’re going to choose number 3, scroll to it. We’re gonna add it. Alpha 1 alpha 3. And the next point is 0, 3 so we’re going to use 0 and then the question mark here, number 1
we’re going to enter number 3, alpha 3. And again, we look and see if we have entered correctly, and we have. Enter umber 1 or scroll to it. We’re going to set up the Green’s Theorem. Double integral 01 in three x Notice this, if you do the vertices and put it on a piece of paper notice that the line here is an angle such as this where certain parameters and this is the y function remember the y equals mx+b that you learned in Algebra? Well the mx is the slope and of course 3 over 1 is the slope of this line. So if you graphed it, you’d put 3x into the Y function on your graphing calculator and that would be the angle just like this. And then of course we have 3 over 0 and then 3 down the origin of the graph. So that’s the triangle we’re working with. And we’re going to integrate this right here with respect to Y and over this range here. And that equals this over the range. We take the 3x and put it in for all the y’s and we come up with 72 x to the 4 and then 0 of course is a 0. And upper minus lower is 72 x to the fourth. Now we’re going to integrate that with respect to x over this range here which equals 72x to the 5. Remember we add 1 to the exponent and divide by 5. That exponent in the problem. And over this range here. Remember Newton and Leibniz were working on exponents in the sixteen hundreds, that’s how they came up with calculus and of course logarithms, also. Logarithms is an exponent. And so we’re gonna do that range at X equals one. we substitute that for the x, come up with this, and the answer is 72 over 5 square units. 14.4 square units. Pretty neat, huh? everystepcalculus.com. go to my site buy my programs. It’s the best deal around. Much, much more economical and worth worth it then they even the calculus book. So enjoy my program and pass calculus or physics. Have a good one!