Solve the Problem $z = f ( x , y )$

question 33

Essay

Solve the problem.
-For the surface $z = f ( x , y )$ , show that the surface integral $\iint g ( x , y , z ) d \sigma =$ $\iint \mathrm { g } ( \mathrm { x } , \mathrm { y } , \mathrm { f } ( \mathrm { x } , \mathrm { y } ) ) \sqrt { \left[ \mathrm { f } _ { \mathrm { x } } ( \mathrm { x } , \mathrm { y } ) \right] ^ { 2 } + \left[ \mathrm { f } _ { \mathrm { y } } ( \mathrm { x } , \mathrm { y } ) \right] ^ { 2 } + 1 } \mathrm { dx } d y$

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