Question

Find the mass of the triangular region with vertices (0, 0), (4, 0), and (0, 6), with density function ρ(x,y)=x^2+y^2.

Answer 1

are you looking for a cool change of variable [off the cuff, dunno]; or just how to process it [i can help] as a double integration


actually physically drawing the triangle will make the integration limits seem more obvious.

Answer 2

Ya I realized this after I've solve it aha . I was looking for the bounds, been a long day and felt kind of lazy but after I say down and looked at it I got it.

Answer 3

\[\Large M = \int\limits_{y=0}^{y=6} \; \int\limits_{x=0}^{ 4-\frac{2}{3}y} dx \, dy \qquad \rho(x,y)\]
\[\Large = \int\limits_{y=0}^{y=6} \; \int\limits_{x=0}^{ 4-\frac{2}{3}y} dx \, dy \qquad x^2 + y^2\]


http://www.wolframalpha.com/input/?i=int_%7Bx%3D0%7D%5E%7B4%7D++int_%7By%3D0%7D%5E%7B+6-%283%2F2%29x%7D++%28x%5E2+%2B+y%5E2%29+dy+dx+

http://www.wolframalpha.com/input/?i=int_%7By%3D0%7D%5E%7B6%7D++int_%7Bx%3D0%7D%5E%7B+4-%282%2F3%29y%7D++%28x%5E2+%2B+y%5E2%29+dx+dy+#

Answer 4

ie
\[\Large = \int\limits_{x=0}^{4} \; \int\limits_{y=0}^{ 6-\frac{3}{2}x} dy \; dx \qquad x^2 + y^2\]