The hemisphere , is parametrised by
where and .
The normal vector is
and
.
Therefore
.
first picture is all the questions that need to be answered, second is the actual numbers...
Evaluate the surface integrat S «..z) ds using a parametric description of the surface S f(x,y.z) = x2 +y? where S is the hemisphere x² + y² + z = 4, for z 20 Write a parametric description of the given hemisphere using u = p and v=0. rſu v)=000 where O susandsvs (Type exact answers.) The value of the surface integral is (Type an exact answer.)
Evaluate the surface integral f(x,y,z) dS using a parametric description of the surface. 2 f(x,y,z) x 2 where S is the hemisphere x + y +z2 = 25, for z 2 0 The value of the surface integral is (Type an exact answers, using t as needed.) Evaluate the surface integral f(x,y,z) dS using a parametric description of the surface. 2 f(x,y,z) x 2 where S is the hemisphere x + y +z2 = 25, for z 2 0 The...
2. Evaluate the surface integral [[Fids. (a) F(x, y, z) - xi + yj + 2zk, S is the part of the paraboloid z - x2 + y2, 251 (b) F(x, y, z) = (z, x-z, y), S is the triangle with vertices (1,0,0), (0, 1,0), and (0,0,1), oriented downward (c) F-(y. -x,z), S is the upward helicoid parametrized by r(u, v) = (UCOS v, usin v,V), osus 2, OSVS (Hint: Tu x Ty = (sin v, -cos v, u).)...
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
Evaluate the surface integral f(x,y,z) dS using a parametric description of the surface. f(xyz) = 4x, where S is the cylinder X + z2-25, 0 ys2 The value of the surface integral is (Type exact answers, using T as needed.) Find the area of the following surface using the given explicit description of the surface. The cone z2 = (x2 +y2) , for Oszs8 Set up the surface integral for the given function over the given surface S as a...
This Test: 18 pts possible 5 of 18 (1 comnplete) the foillowing vector field and region. Check for agreement Evaluate both integrals of the Divergence Theorem D= (xy.z): x2 + y2 + 22 s9) F (4x,3y,32); the Divergence Theorem. Select the correct choice below and fill in any answer boxes within your choice. Set up the volume integral OA !!! dp do d8, where the integrand does not simplity to a constant 0 0 O B. The integral simplifies to...
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.
Give a parametric description of the form r(u, v) = (x(u,v),y(u,v),z(u,v)) for the following surface. The cap of the sphere x² + y2 + z = 36, for 3/3 sz56 Select the correct choice below and fill in the answer boxes to complete your choice. (Type any angle measures in radians. Use angle measures greater than or equal to 0 and less than 21. Type exact answers in terms of ..) A. Fu.v) = (6 sin u cos V,6 sin...
3. Verify Stokes' Theorem for the vector field F(x, y, z)= (x2)ĩ+(y2)]+(-xy)k where S is the surface of the cone +y parametrized by (u,v)-(ucos v, u sin v, hu) x2+y2 a at height h above the xy-plane Z = a V 0<vsa, OSvs 2n, and as is the curve parametrized by ē(f) =(acost,asint, h), 0sis27 as x2+ a 3. Verify Stokes' Theorem for the vector field F(x, y, z)= (x2)ĩ+(y2)]+(-xy)k where S is the surface of the cone +y parametrized...
Hw32-16.7-Surface-Integrals: Problem 1 Problem Value: 1 point(s). Problem Score: 67%. Attempts Remaining: 22 attempts. Help Entering Answers (1 point) Evaluate the surface integral 4xyz ds. Where S is the cone with parametric equations x = u cos(u), y = u sin(u), z = u and 0 <u< 4,0 4xyz ds = [” [“ aunscos()+sin(Sqrt2un2cos^2 I du du Jui Jui where 4 мммм = 3pi/2 Evaluate 4xyz ds = JJ s If you don't get this in 3 tries, you can...