Question

\[\int\limits_{c}^{d} \int\limits_{a}^{b} (d^2f)/(dxdy) dxdy\] equal?

Answer 1

okay the answer is f(b,d)-f(b,c)-f(a,d)+f(a,c)

Answer 2

right?

Answer 3

could you please rewrite the question??

Answer 4

\[\int\limits_{c}^{d} \int\limits_{a}^{b} (d^2f)/(dxdy) dxdy\] equal?

Answer 5

Is it ??
\[ \int\limits_{c}^{d} \int\limits_{a}^{b} \frac{d^2f}{dxdy} dxdy\]
or partials??

Answer 6

integrate the Partials derivaties

Answer 7

how the original format?

Answer 8

\[ \int\limits_{c}^{d} \int\limits_{a}^{b} \frac{\partial^2f}{\partial x\partial y} dxdy \]

Answer 9

how did you type the dividing and the partical ^^?

Answer 10

\frac{numerator}{ denominator }
\( \partial \) \partial
and my super secret technique ... click left, "Show Math as" => "Text Commands"
then copy anything

Answer 11

\partial x \frac{1}{x}

Answer 12

[\partial x] , [\frac{1}{x}]

Answer 13

Wow not only did I get beat to the answer but I learned a new formatting technique for this website, thank experimentX, you get a medal from me too :P

\[\frac{numerator}{ denominator}\]

Answer 14

note* This is just a try ...
\[ \int\limits_{c}^{d} \int\limits_{a}^{b} \frac{\partial^2f}{\partial x\partial y} dxdy =
\int\limits_{c}^{d} \left ( \int\limits_{a}^{b} \frac{\partial }{\partial x}
\left ( \frac{\partial f}{\partial y} \right ) dx \right ) dy
\]

@OsmondF \[ at the beginning

Answer 15

Test?

\[\int\limits\limits_{c}^{d} \int\limits\limits_{a}^{b} \frac{\partial^2f}{\partial x\partial y} dxdy = \int\limits\limits_{c}^{d} \left ( \int\limits\limits_{a}^{b} \frac{\partial }{\partial x} \left ( \frac{\partial f}{\partial y} \right ) dx \right ) dy\]

Answer 16

Lol ... perfect!!

Answer 17

Oh! That is nifty, but did you question get answered sufficiently OsmondF?

Answer 18

where has "show text" ..

Answer 19

right click?

Answer 20

Yep!

Answer 21

\int\limits\limits_{c}^{d} \int\limits\limits_{a}^{b} \frac{\partial^2f}{\partial x\partial y} dxdy = \int\limits\limits_{c}^{d} \left ( \int\limits\limits_{a}^{b} \frac{\partial }{\partial x} \left ( \frac{\partial f}{\partial y} \right ) dx \right ) dy

Answer 22

""Show Math as" => "Text Commands" then copy anything" <-- there's a pop-up menu for it

Answer 23

Ah you got to add the \[

Answer 24

\[ at front

Answer 25

and \] at back

Answer 26

\[\int\limits_{c}^{d} \int\limits_{a}^{b} \frac{\partial^2f}{\partial x\partial y} dxdy = \int\limits_{c}^{d} \left ( \int\limits_{a}^{b} \frac{\partial }{\partial x} \left ( \frac{\partial f}{\partial y} \right ) dx \right ) dy

Answer 27

Don't forget to close the syntax tag too! :D

Answer 28

\[\int\limits\limits_{c}^{d} \int\limits\limits_{a}^{b} \frac{\partial^2f}{\partial x\partial y} dxdy = \int\limits\limits_{c}^{d} \left ( \int\limits\limits_{a}^{b} \frac{\partial }{\partial x} \left ( \frac{\partial f}{\partial y} \right ) dx \right ) dy\]

Answer 29

Horray!

Answer 30

\[ \int\limits\limits_{a}^{b} \frac{\partial }{\partial x} \left ( \frac{\partial f}{\partial y} \right ) dx = \left [ \frac{\partial f}{\partial y}\right ]_a^b = \frac{\partial }{\partial y} f(b, y) - \frac{\partial }{\partial y} f(a, y)\\

\text{ So we have , } \\

\int_c^d \left (\frac{\partial }{\partial y} f(b, y) - \frac{\partial }{\partial y} f(a, y) \right ) dy = \\
\int_c^d \frac{\partial }{\partial y} f(b, y) dy - \int_c^d \frac{\partial }{\partial y} f(a, y) dy =
f(b,d) - f(b,c) - (f(a,d) - f(a,c))
\]

Answer 31

There you go!!