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.