Compute the scalar suface integral z z k z ds where k is the part of the sphere of radius 3 centered at the origin, that lies in the first octant. (hint: use the parametrization g(θ, φ) = h3 sin φ cos θ, 3 sin φ sin θ, 3 cos φi with domain of definition [0, π/2] × [0, π/2])

With the parameterization

take the normal vector to to be

which has magnitude

Then the integral is

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.

it’s supposed to be -4+45=41

step-by-step explanation: