Question

\[\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 1

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