Question

I got stucked in there (2nd photo)

12. Evaluate the surface integral IK 25-x'-y2 dS where S is the hemisphere centered at the origin with radius 5, for z20. 2) Evaluate the centered at the onqin wth radius S, o 220 a1 5(25-x-yds where S Is The hemisphere Tn Polar form 2. 2. 2 V2S-T

Answer 1

12. Evaluate the surfaceintcgral15--crd with radius 5, for z20 Here is the parameterization for this sphere Since we are working on the upper half of the sphere here are the limits on the parameters Next, we need to determine rθ γφ. Here are the two individual vectors r, (θ, φ)--5sin φ sǐηθι +5 sin φ cos@j Now let's take the cross product. Finally, we need the magnitude of this, /25 sin2ιρ (sin20+ cos24 ー 5sin φ Here is the evaluation for the double integral 25 cos'p (5 sin p) dA 125 cosip sin p dp dθ 0 2m (-125 cos(p))lǐde = 0 2T 125 de 0 250 π