- #1
Mdhiggenz
- 327
- 1
Homework Statement
∫∫x2dA; R is the region in the first quadrant enclosed by
xy=1, y=x, and y=2x.
First thing I did was notice that I had to find dydx, then
I graphed y=1/x, y=x, and y=2x.
Graphing I say that the limit of dy lie between x≤y≤2x
However I get confused as to how they want us to find dx.
My first approach was to use y=1/x and y=x and set them equal to each other, and solve for x. Doing so I get x2=1 or x = 1 getting only positive values since it lies in the first quadrant.
then I use set y=1/x, and y=2x equal to each other, and solve for x ; 1/x=2x thus giving me
x=√(2)/2.
Here is where I get confused the dx limit goes from 0≤x≤√(2)/2
I understand that dx would be the maximum value of x which is √(2)/2, but why wouldn't it be 1.
Also now giving it some thought, why did they choose to use 1/x and equal it to the other values, and not the graph of 2x or x?
Thanks