Question

EXTRA: 16.7 Change of Variables in Multiple Integrals Use the change of variables $x = 3u + 3v$ and $y = 3u - 3v$ to evaluate the integral $\iint_R \sqrt{x - y} \, dA$ where the region of integration $R$ in the $xy$ plane is the square with vertices $(0,0)$, $(3,3)$, $(6,0)$, $(3, -3)$. Hint: This is similar a problem in your homework in 16.7 Change of Variables in Multiple Integrals. But in this case, I gave you the region $R$. Also, the integrand is different. Not hard, just different. a. Sketch the new region $S$ in the $uv$ plane using the the given change of variable and find the limits of integration for the new integral with respect to $u$ and $v$. b. Compute the Jacobian $J(u, v)$. c. Change variables and evaluate the new integral. Give an exact value.

          EXTRA:
16.7 Change of Variables in Multiple Integrals
Use the change of variables $x = 3u + 3v$ and $y = 3u - 3v$ to evaluate the integral
$\iint_R \sqrt{x - y} \, dA$
where the region of integration $R$ in the $xy$ plane is the square with vertices $(0,0)$, $(3,3)$, $(6,0)$, $(3, -3)$.

Hint: This is similar a problem in your homework in
16.7 Change of Variables in Multiple Integrals. But in this
case, I gave you the region $R$. Also, the integrand is
different. Not hard, just different.
a. Sketch the new region $S$ in the $uv$ plane using the the given change of variable and find the limits of
integration for the new integral with respect to $u$ and $v$.
b. Compute the Jacobian $J(u, v)$.
c. Change variables and evaluate the new integral. Give an exact value.

EXTRA:
16.7 Change of Variables in Multiple Integrals
Use the change of variables x = 3u + 3v and y = 3u - 3v to evaluate the integral
√(x - y) dA
where the region of integration R in the xy plane is the square with vertices (0,0), (3,3), (6,0), (3, -3).

Hint: This is similar a problem in your homework in
16.7 Change of Variables in Multiple Integrals. But in this
case, I gave you the region R. Also, the integrand is
different. Not hard, just different.
a. Sketch the new region S in the uv plane using the the given change of variable and find the limits of
integration for the new integral with respect to u and v.
b. Compute the Jacobian J(u, v).
c. Change variables and evaluate the new integral. Give an exact value.

Added by John C.

Question

Please give Ace some feedback