Sketch the domain d bounded by y = x^2, y = (1/2)x^2, and y=6x. use a change of variables with the map x = uv, y = u^2 (for u ? 0) to calculate double integral dy^ - 1dx dy. this is an improper integral since f(x, y) = y^ - 1 is undefined at (0, 0), but it becomes proper after changing variables.

Under the given transformation, the Jacobian and its determinant are

so that

where is the region transformed into the - plane. The remaining integral is the twice the area of .

Now, the integral over is

but through the given transformation, the boundary of is the set of equations,

We require that , and the last equation tells us that we would also need . This means and , so that the integral over is

side side side

side angle angle

angle side angle

side angle side

step-by-step explanation:

answer: c.  

step-by-step explanation:

mixtures containing substances that get attracted to magnet can be separated using a magnet. we can separate iron from a mixture of sand and iron, as only iron attracts to the magnet.