Answer:
The answer is 7.25. That is there will be no change.
Step-by-step explanation:
The equations of differential vector transformation from the v-u plane to the x-y plane is given by,
![\left[\begin{array}{ccc}dx\\dy\end{array}\right] = \left[\begin{array}{ccc}dx/dv&dx/du\\dy/dv&dy/du\end{array}\right] \left[\begin{array}{ccc}dv\\du\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Ddx%5C%5Cdy%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Ddx%2Fdv%26dx%2Fdu%5C%5Cdy%2Fdv%26dy%2Fdu%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Ddv%5C%5Cdu%5Cend%7Barray%7D%5Cright%5D)
where the square matrix given is the Jacobian matrix and we can evaluate it by differentiating the equation for x and y given in the question by v and u and we will obtain the following matrix,
.
Differential area transformation from v-u coordinate system to the x-y coordinate systen is given by,

where Det(J), is evaluated as below,

which we plug into the above equation to obtain,

in part b) area of the region D in the u-v plane is given as 7.25 that is dvdu=7.25 , that means according to the above equation that the area of the corresponding transformed region in the x-y plane that is dxdy will also be the same according o the above equation,So,
