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Points) Suppose R is the triangle with vertices (~ 1,0). (0, 1), and (1,0) (a) As an iterated integral, (Sx + 3y)? dA = EI' (Sx + 3y)? dx dy with llmits of int...

Question

Points) Suppose R is the triangle with vertices (~ 1,0). (0, 1), and (1,0) (a) As an iterated integral, (Sx + 3y)? dA = EI' (Sx + 3y)? dx dy with llmits of integration(b) Evaluate the integral in part (@). Hint: substitution may make the Intogral easier: Integral

points) Suppose R is the triangle with vertices (~ 1,0). (0, 1), and (1,0) (a) As an iterated integral, (Sx + 3y)? dA = EI' (Sx + 3y)? dx dy with llmits of integration (b) Evaluate the integral in part (@). Hint: substitution may make the Intogral easier: Integral



Answers

For Exercises $29-33,$ evaluate the integral. $\int_{R}(2 x+3 y)^{2} d A,$ where $R$ is the triangle with vertices at $(-1,0),(0,1),$ and (1,0)

This question we have immigration X and boundaries is x zero 01 off X y lost four white or three The X Taking the first integration. We will have integration from 0 to 1 ex wife plus point for food and our boundaries is X and zero course the ax taking or substituting by these boundaries, we will have duration 01 negative exports. Three in us or four the x by taking another integration. Now we will have negative export 4/4, thus export five Work five and our limits zero and one. If we substitute by these limits, we would have a negative 1/4 loss over five zero The Seattle, which is equal negative line over 20.

We need to serve the integral What two x y plus put away for three d eight We're are is the region Bone did boy. But this he's 00 10 and zero. Here we can consider the area. What's more addicting get D A equals The X Times doing so this never lenticular who were are who x y plus four y about three d a. It works double integer from 0 to 1 and from Wally, a quick fix oy equals zero off to exploit. Thus, for wife or three D, that equals the integrity from 0 to 1. Well, x y squared What's boy More boy equals X Roy equals zero gigs. The sequence figure from 0 to 1. Well next times zero square off zero for four minus X times exist Squid minus X for four dx The sequence digger from 0 to 1 well minus x for three minus X or fear gigs. The sequence six or four before my sticks for you from 0 to 1, which equals 1/4 minus one word for you. Zero for four plus zero. So the double integral we're off to exploit less corduroy or three d A equals minus nine over time. Thank you

So you screen serum the value we first right. His area into group the ripped him off. This with respect to X. So two X minus the rip people this extra Plus why square with respect to why so two? Why d a And we try to figure out So the area zero zero next to why one x zero y one. So it goes like this and the Richard is like this. So this lie from zero zero two to one should be. Why? Because, uh, one over to x. So this integral. Why? From one over to ex to one and x from zero to two two x minus two y Why First and X, we are two x y minus y square one over to X two won t x. So if we probably why? Because one we had two X minus one. Probably. Why was one over to X? We get minus X squared, plus one over four square. So zero to two minus three over for X square plus two x minus one, some minus X cube over for plus square minus X. So we're probably to open zero. We don't We don't have anything So we just have a problem too. S O miners eight over. Force minus two plus exclusives. Two scores for And the miners too. And that keeps our cereal.

Okay, problem. 24. I have three points and we want to. They're going to grow from the counter clockwise around the triangle here. So there are three pars. The first part, Ari's equals two from year ago to one girl. So that's t zero. He from Europe One on one 10201 So that's one Manistee. He he is also from 01 and okay, to start one from 012 heroes girl. So that's 01 dynasty. Right? Okay, So the total which would the pro for three times for some axes. Just tea. And why the hero from one? Ah, the ex. Yeah, so that just gt So that's one over two. Hold a second. You guys just zero, right, You guys hero. So this term does not exists for part one apart too. We have X minus y So is from 01 axe minus y. And the extra practice might speed he right, Linus here, Okay. And plus X plus y plus X plus y. And he wiII it just did. He so have this. You have a one minus two piece 02 minus one plus one to t d t That's also what TDD right, This one on third, he actually just year old soldiers. That's plus why one person, one dynasty and the wise mine STT So I just e here we have ah t minus one as, like this one. So it's minus one, huh? Add them up. Get one for the total answer, right?


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