Question

Evaluate the double integral ye^x dA, where R is the triangular region with vertices (0, 0), (4, 4), and (6, 0).

Answer 1

@ganeshie8 @iambatman @wio @Loser66 @Destinymasha @paki @Compassionate @Kainui

Answer 2

As a start, sketch the region in xy plane

Answer 3

For this problem, you need change a little bit,
the equation of the line OA is x =y
the equation of the line AB is y = -2x+12 or \(x= 6-\dfrac{y}{2}\)
and fixed y, limit from 0 to 4
Hence your integral is
\[\int_0^4\int_{y}^{6-(y/2)} ye^xdxdy\]

Answer 4

How did you get y=-2x+12?

Answer 5

find out the slope of the line by formula \(\dfrac{y-y_0}{x-x_0}\) then plug back to the equation of the line y = mx +b to get it

Answer 6

Don't get??

Answer 7

Ok, 2 points (4,4) , (6,0) , hence the slope \(m =\dfrac{y-y_0}{x-x_0}=\dfrac{0-4}{6-4}=-2\)
pick one of the point to plug in the equation, I pick (6,0) , hence \( y = mx +b \\0= -2*6+b\\b= 12\\put ~~back\\y =-2x+12\\x=6-\dfrac{y}{2} \)

Answer 8

got to go. Good luck

Answer 9

But how did you get x=y?