Finding Centroid of Triangle in First Quadrant

[magma_saber]

Homework Statement

Find the centroid of the triangular region in the first quadrant bounded by the line 4x+y=4, the x-axis, and the y-axis.

Homework Equations

\int\int\deltadA
xbar = My/M
ybar = Mx/M

The Attempt at a Solution

Is the boundary for the dy from 0 to 4, and dx from 0 to 4-4x?

 

[vela]

No, your limits for x can't contain x. They can only depend on y.

 

[magma_saber]

so its y-4/4?
also are my limits for dy correct?

 

[vela]

No, that's not quite correct either. (I assume you mean (y-4)/4, not y-1.) You should always plug in a few values to do a sanity check. In this case, when y=0, you'd get a negative answer.

Your limits for y are fine. (But I'll note I'm saying this under the assumption that you set things up correctly.)

Did you draw a sketch of the region of integration?

 

[magma_saber]

the region would be the triangle from y=4 to y=0 and x=0 and x=1 right?
and is the limit 4-4x?