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Let T be the triangular area in R? with vertices {(0,0), (-1,),(1,3)}. Use the transformation 31)/4to calculate f fk+x4+-s)dxdy: (6 pts )(+nr...

Question

Let T be the triangular area in R? with vertices {(0,0), (-1,),(1,3)}. Use the transformation 31)/4to calculate f fk+x4+-s)dxdy: (6 pts )(+nr

Let T be the triangular area in R? with vertices {(0,0), (-1,),(1,3)}. Use the transformation 31)/4to calculate f fk+x4+-s)dxdy: (6 pts ) (+nr



Answers

Use the given transformation to evaluate the integral.
$$\begin{array}{l}{\int_{R}(x-3 y) d A, \text { where } R \text { is the triangular region with }} \\ {\text { vertices }(0,0),(2,1), \text { and }(1,2) ; \quad x=2 u+v} \\ {y=u+2 v}\end{array}$$

Tell over Bolivia. Going pills are problem number man from the section my temple in digress. This question is doesn't obviously clearly but we're to start when we can start with you see what we can skin slur angle Okay. In this case, one can go This is our is our Now we have a market points This is origins zero a little These acts issue this can be be this point is fun park So exactly little my axes Mark Little liar So impressions What are the questions that will be happy that it from you we called zero do V equals are the sequence You you lose the relation X equals used square with musicals there was quite legit they could and by equals b seaQuest But why he calls me Because you but musical group X that is it comes to be like this is like Ok so what will be the points here? Barton work Okay, it is learned zero mark this one zero comma zero No. 11 is 11 is forward by then. Like Equus Group X which is called smart. That is eggs because look or ex because you square Matilda kowtow one square, Which is it? Thank you. Don't question Thank you

Today we're going to solve for the number nine the triangular regions with notices 00 zero comma one and one common one. It's shown on the right. This is the triangle, So Okay, there was a triangle that we have We need to param address each side of the triangle first side from they're all comma 02 zero comma one Absolutely. You equals zero and we equals p were zero Lazaro Ricardo t lasagna record one. Under the transformation, X equals u squared. Why you closely? We have X equals u squared equals zero and y equals v equals t. Therefore, we get X equal to zero on why Equal Tau teach the zero less than a regular t less than or equals one. The second is from side zero comma one don't one comma one substitute you equal city and we equals one zero less than a record dirty less than article smart. Under the transformation, X equals you square and y equals V. We have X equals. U squared equals peace Quit And why? Because Greek Because what so we get like X equals t square? And why? Because one it's Amos vehicles one. Then the third is from the side one comma one, 20 comma zero u equals one minus T vehicles one dynasty zero less than or equal duty less than articles one under the transformation X equals you square and why equals three? We have X equals U squared equals one minus t the whole square. And why equals V equals one minus tape The four we got like X equals one minus t the whole square. And why equals one minus t zero less than or equal to t less than recalls. Smart. So we have noticed that X equals y square. The image on the side is a graph off X equals y square for zero lesson recorded by less than records one or the graph. Why? Because protects for zero Latina re cortex lateral record. The one for the two graphs. Yeah, for these two graphs on the left is still the This is a triangular region with the sides and if colors and on the right side of the graph off the image after transformation, this is transformation graph. So the answer and off our question. Thank you

The problem. This use the Cuban transformation. Teo wanted it into the role your art is The anchor region with lettuce is zero to want one too. The transformation is actually I wanted to. You has Bean. Why is it what you pass to it? So first that's cash the region are you know you one and I want to but this is a region Are the original car is bonded by why you could to half axe why you want to Two packs and x plus y It's equal to three They're from the transformation we're half the region has it's funded by you equal to zero. Be equal to zero you plus V. It's equal to what? Three five sketch Picture your feet. This is us on behalf and to grow It's a control into girl from zero two one throw from zero to one month's being X minus three. Why, yes, He called to negative you wass and then times harsh wax Why you be which is equal to three This task three you you be bench is untrue. Three halves into grew from zero to one negative one wants to be a squire minus five. Ham's one minus three. You feel you just write down the author. This is a two ninety three

The problem is finding the image of the touch us and the given transformation as is a track angular region with readies. Zero zero one one zero one axe physical to your squire wise it could be a way. So look up this figure. Zero zero one one Seirawan No, this is us. Now let's you is equal to zero. Half axe is equal to zero. Among three is a good one. Half Why is thick with what? Ugh it access because, as you know, is why Axis? Why would I want this? It's my why I could want on DH here. This is you going to be. Then we have Axe is equal to y squared. No, what squire is able to acs So you're not this region. Bye r and our is the image of the sat s on. There's a given transformation


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