Question

find the mass of the bar [AB] if the density function is f(x,y)=x. coordinates: A(1,0) B(3,1) it has to be a double integral

Answer 1

could you clarify your question more? i'm confused

Answer 2

i have to make up a integral using the coordinates of the bar and the density. i dont't remember the formula for the mass of a bar using integrals.

Answer 3

are we looking to do a double integral here?

volume / density = mass

Answer 4

yes

Answer 5

is this bar a cylinder? because we can just put our f(x,y) into cylindrical coordinates and then solve for mass

Answer 6

m=∫∫Dρ(x,y)dA D is the domain of the bar. i can't use it as a cylinder. i found the formula but i'm still a little bit confused. dA is i remember right is sqrt of x^2+y^2

Answer 7

\[\int\limits_{1}^{3}\int\limits_{0}^{1} x dy dx= \int\limits_{1}^{3} x dx =\frac{ 3^2 }{ 2 }-\frac{ 1^2 }{2}=\frac{ 9-1 }{ 2 }-\frac{ 8 }{2}=4\]

Answer 8

is this correct?

Answer 9

in rectangular coordinates i don't remember any x^2 +y^2 for my jacobian... but that may be because i never really answered questions in rectangular

Answer 10

http://math.stackexchange.com/questions/254247/mass-and-center-of-mass-of-lamina-in-polar-coordinates