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Evaluate the surface integral SS -?yds Where S :r(u, v) = 5 cosui +5sinu j+ vk,...
Evaluate the surface integral. y ds, S is the helicoid with vector equation r(u, v) = (u cos(V), u sin(), v), OSUS 4,0 SV S.
10. Evaluate the integral le z ds, where S is given by r(u, v) = (u + v)i + (u – v)j + sin v k, Osus2, 0505
SS zds, s 0:3 evaluate the surface integral where is the cone z = V x² + y2 between the xy-plone and le colid s cut z = 2.
Evaluate the surface integral. 1 (x + y + z) ds, S is the parallelogram with parametric equations x = u + v, y = u - v, z = 1 + 2 + v, osus 6, Osvs 2.
Evaluate the surface integral. (x + y + z) ds, S is the parallelogram with parametric equations x = u + v, y = u – v, z = 1 + 2u + v, Osus 6, 0 SV 53. Is
8) [10 points] Use a surface integral to find the mass of the surface lamina Зл r(u, v)=sin v cosui+sin vsin uj+cos vk where Osus 05 vsa and density is given by 2 P(x,y,z)= x² + y2 +2?. Ba
3. (3 points) Let the surface S be parametrized by r(u, v) = (bcos u, sin u, v) for (u, v) E D where D = {(u, v) O SUST, SU <3}. Set up the iterated integral, but do not evaluate, the surface area JJsdS (I want the iterated integral for du du, and in that order. Do not even try to evaluate this integral!).
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 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...
v e, v, z)dzdydz where f(e.v.)3 Evaluate the triple integral D and Triple Integral Region R Remember that: H(u, t, u)|J(u, v, w)ldududu F(z, y, z)dV Preview t lower limit Preview น upper limit- U lower limit Preview upper limit w lower limit upper limit H(u, o, w)- Preview Preview Ila Preview H(u, e, w)J(u,v, wdudedu Hint: The focus of this problem is on evaluating the integral and using the Jacobian. v e, v, z)dzdydz where f(e.v.)3 Evaluate the triple...
Assume that is the parametric surface r= x(u, v) i + y(u, v) j + z(u, v) k where (u, v) varies over a region R. Express the surface integral 116.3.2) as as a double integral with variables of integration u and v. a (x, y) a(u, v) du dy ru Хry dy du l|ru Xr, || f (x (u, v),y(u, v),z (u, v)) 1(xu, Wsx,y,z) Mos u.v.gou,» @ +()*+1 li ser(u, v),y(u, v),z (u, v) Date f (u, v,...