Answer:
188
Step-by-step explanation:
10*5*4 - 6*2
Answer:
6 ?
Step-by-step explanation:
I think the answer is
-14m^2 + 15m - 3
(The ^2 is squared)
The circle equation is in the format (x – h)2 + (y – k)2 = r2, with the center being at the point (h, k) and the radius being "r".
Therefore the center is: (6,-5)
Answer:

Step-by-step explanation:
Given




Required
Evaluate
Let:


Add both equations


Subtract both equations


So:


R is defined by the following boundaries:
, 






So, we can not set up Jacobian
![j(x,y) =\left[\begin{array}{cc}{\frac{du}{dx}}&{\frac{du}{dy}}\\{\frac{dv}{dx}}&{\frac{dv}{dy}}\end{array}\right]](https://tex.z-dn.net/?f=j%28x%2Cy%29%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%7B%5Cfrac%7Bdu%7D%7Bdx%7D%7D%26%7B%5Cfrac%7Bdu%7D%7Bdy%7D%7D%5C%5C%7B%5Cfrac%7Bdv%7D%7Bdx%7D%7D%26%7B%5Cfrac%7Bdv%7D%7Bdy%7D%7D%5Cend%7Barray%7D%5Cright%5D)
This gives:
![j(x,y) =\left[\begin{array}{cc}{1&1\\1&-1\end{array}\right]](https://tex.z-dn.net/?f=j%28x%2Cy%29%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%7B1%261%5C%5C1%26-1%5Cend%7Barray%7D%5Cright%5D)
Calculate the determinant



Now the integral can be evaluated:
becomes:



So:



Remove constants

Integrate v


![\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2}\int\limits^6_0 [e^{u*7} - e^{u*0}]du](https://tex.z-dn.net/?f=%5Cint%5Climits%20%7B%5Cint%5Climits%20%7B7%28x%20%2B%20y%29e%5E%7Bx%5E2%20-%20y%5E2%7D%7D%20%5C%2C%20dA%20%3D%20%5Cfrac%7B7%7D%7B2%7D%5Cint%5Climits%5E6_0%20%20%5Be%5E%7Bu%2A7%7D%20-%20%20%20e%5E%7Bu%2A0%7D%5Ddu)
![\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2}\int\limits^6_0 [e^{7u} - 1]du](https://tex.z-dn.net/?f=%5Cint%5Climits%20%7B%5Cint%5Climits%20%7B7%28x%20%2B%20y%29e%5E%7Bx%5E2%20-%20y%5E2%7D%7D%20%5C%2C%20dA%20%3D%20%5Cfrac%7B7%7D%7B2%7D%5Cint%5Climits%5E6_0%20%20%5Be%5E%7B7u%7D%20-%20%20%201%5Ddu)
Integrate u
![\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2} * [\frac{1}{7}e^{7u} - u]|\limits^6_0](https://tex.z-dn.net/?f=%5Cint%5Climits%20%7B%5Cint%5Climits%20%7B7%28x%20%2B%20y%29e%5E%7Bx%5E2%20-%20y%5E2%7D%7D%20%5C%2C%20dA%20%3D%20%5Cfrac%7B7%7D%7B2%7D%20%2A%20%5B%5Cfrac%7B1%7D%7B7%7De%5E%7B7u%7D%20-%20%20%20u%5D%7C%5Climits%5E6_0)
Expand
![\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2} * ([\frac{1}{7}e^{7*6} - 6) -(\frac{1}{7}e^{7*0} - 0)]](https://tex.z-dn.net/?f=%5Cint%5Climits%20%7B%5Cint%5Climits%20%7B7%28x%20%2B%20y%29e%5E%7Bx%5E2%20-%20y%5E2%7D%7D%20%5C%2C%20dA%20%3D%20%5Cfrac%7B7%7D%7B2%7D%20%2A%20%28%5B%5Cfrac%7B1%7D%7B7%7De%5E%7B7%2A6%7D%20%20-%206%29%20-%28%5Cfrac%7B1%7D%7B7%7De%5E%7B7%2A0%7D%20-%20%200%29%5D)
![\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2} * ([\frac{1}{7}e^{7*6} - 6) -\frac{1}{7}]](https://tex.z-dn.net/?f=%5Cint%5Climits%20%7B%5Cint%5Climits%20%7B7%28x%20%2B%20y%29e%5E%7Bx%5E2%20-%20y%5E2%7D%7D%20%5C%2C%20dA%20%3D%20%5Cfrac%7B7%7D%7B2%7D%20%2A%20%28%5B%5Cfrac%7B1%7D%7B7%7De%5E%7B7%2A6%7D%20%20-%206%29%20-%5Cfrac%7B1%7D%7B7%7D%5D)
Open bracket
![\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2} * [\frac{1}{7}e^{7*6} - 6 -\frac{1}{7}]](https://tex.z-dn.net/?f=%5Cint%5Climits%20%7B%5Cint%5Climits%20%7B7%28x%20%2B%20y%29e%5E%7Bx%5E2%20-%20y%5E2%7D%7D%20%5C%2C%20dA%20%3D%20%5Cfrac%7B7%7D%7B2%7D%20%2A%20%5B%5Cfrac%7B1%7D%7B7%7De%5E%7B7%2A6%7D%20%20-%206%20-%5Cfrac%7B1%7D%7B7%7D%5D)
![\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2} * [\frac{1}{7}e^{7*6} -\frac{43}{7}]](https://tex.z-dn.net/?f=%5Cint%5Climits%20%7B%5Cint%5Climits%20%7B7%28x%20%2B%20y%29e%5E%7Bx%5E2%20-%20y%5E2%7D%7D%20%5C%2C%20dA%20%3D%20%5Cfrac%7B7%7D%7B2%7D%20%2A%20%5B%5Cfrac%7B1%7D%7B7%7De%5E%7B7%2A6%7D%20%20-%5Cfrac%7B43%7D%7B7%7D%5D)
![\int\limits {\int\limits {7(x + y)e^{x^2 - y^2}} \, dA = \frac{7}{2} * [\frac{1}{7}e^{42} -\frac{43}{7}]](https://tex.z-dn.net/?f=%5Cint%5Climits%20%7B%5Cint%5Climits%20%7B7%28x%20%2B%20y%29e%5E%7Bx%5E2%20-%20y%5E2%7D%7D%20%5C%2C%20dA%20%3D%20%5Cfrac%7B7%7D%7B2%7D%20%2A%20%5B%5Cfrac%7B1%7D%7B7%7De%5E%7B42%7D%20%20-%5Cfrac%7B43%7D%7B7%7D%5D)
Expand
