Use the parametrization of rphitheta of the sphere of radius

Use the parametrization of r(phi,theta), of the sphere of radius a centered at the origin to find the sphere\'s surface area

THIS IS CALC 3 PLEASE SHOW ALL STEPS

Solution

sphere equation is x ² + y ² + z ² = w² { don\'t have a \'rho\' symbol}

thus f(x,y) = z = ( w² - x ² - y ² )..f_x = - x / z , f_y = - y / z...

and the surface area function is

( 1 + (f_x)² + (f_y)² ) = w / z in this problem..in polar you have r in [ 0 , w ] , in [0 , 2]

for the limits