After sketching the region
it should be clear that you can evaluate the required area as
coold you hekp me solve it by my way
because on the test it not effective to solve it like this
Nice graph! Transgalactic, the point of the u, v substitution is that the curves , and , in the xy-plane, become, in the uv-plane, u= 2, u= 4, and u= 7. Of course, those don't form a bounded figure. That's because, as x and y go to 0, u and v go to infinity. So your integral will be for u= 2 to 4, v= 7 to infinity.
Now, when you substitute for x and y, you also have to substitute for u and v: . And that symbol refers to the determinant, .
In order to find that directly, you would have to solve for x and y in terms of u and v. The hint says you don't have to do that. Find, instead, and take the reciprocal.
i put v to be the vertical axes
and u to be the horizontal axes
so i dont have 7 to infinity
but 0 to 7