Find the area of the surface generated by revolving the curves about the indicated axis. 5) x = sin t, y = 1 + cos t, 0

Q: Evaluate the line integral fc (2 + x*y)s, where C is the half circle x + y? = 1 in the upper half…

A:

Q: Evaluate the surface integral LL 6xzdS where S is the part of the plane 2x + 2y + z = 4 that lies in…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Consider the unit sphere x² + y² + z² = 1. Find the average distance from its north pole to a point…

A: Given: x2+y2+z2=1 It is equation of sphere of radius r=1 unit. We have to find the average distance…

Q: Evaluate f, A.n ds, where A = zi +j- 3y²zk and S is the surface of cylinder x? + y? = 16 included in…

A:

Q: 3. Find the surface area of the surface created when the cylinder y + 2- intersects the cylinder 1²…

A: surface area of the surface given by equation z=f(x,y) A=∫∫Dfx2+fy2+1dA D is the region on xy plane

Q: Suppose a sphere of radius r is sliced by two horizontal planes h units apart (as shown). Show that…

A:

Q: Calculate the line integral ∫Cy2ds, where C is a part of the circle x=acost, y=asint, 0≤t≤π/2.

A:

Q: Evaluate ze*²+y²+z? dV, where E is the portion of the ball centered at the origin of radius 5, x2 +…

A:

Q: Let Yzo.r parametrise a circle with centre zo and radius r (positive orientation). Evaluate the…

A:

Q: Use spherical coordinater to set up the integmal SzdV, the integral SSSz dV, where Q lies between…

A:

Q: Assume a to be a nonzero real no.. Determine the area of the portion of surface xy = az in the fir…

A:

Q: Evaluate the integral eiz dz, (22 + 1)2 where C is the circle |2 + il = oriented anticlockwise.

A:

Q: Use green's theorem to calculate the integral Fdr, F(r, y) = (e* + x²y , e³ – ry² + sen(3) + 2)…

A:

Q: 6. Use Green's Theorem to show that the area of the unit disk x2 + y? <1 in R? is T by evaluating a…

A:

Q: 5. Find the surface area of the portion of the surface z = 2x + y? that is above the triangular…

A:

Q: 1. Find the area of the portion of the plane Зх — Зу + 2 — 12 that lies inside the cylinder y? + 22…

A:

Q: Use SphericalL coerdinates to evaluate the +र |राज्ट | . triple integral SSS x°*y@;=? d V, Where E…

A:

Q: Use Greens Theorem to evalua te the line integral Sr -93 dx +x*dy. where C is the positively onented…

A:

Q: A hole is drilled through the center of a sphere x +y +z? = R,', leaving a ring-shape solid. If the…

A:

Q: The area of the surface p = 2, 0sz<5,0<¢< T is 201 Select one: O True O False

A:

Q: (1) Find the area of the surface of the portion of the cone 2 +y² between the cylinder y? = x and…

A: To find the surface area of cone between given cylinder and plane, use the surface area formula as…

Q: Use Green's Theorem to determine the value of the following line integral 1 I - (7 x + 3 y ) dx + (…

A:

Q: consider surtace S with paramtrization. Gcu,v) = cu,V,uv) , tuts of s also compute the surface areu

A: Given that  G(u,v) = &lt;u,v,uv&gt; , u2+v2≤1 Surface area is given by, S=∫∫D|Gu×Gv|du dv To find Gu…

Q: Use cylindrical coordinates to show that the volume of a sphere of radius a from which a central…

A: If a cylinder of radius b is cut from a sphere of radius a, then the volume of sphere depends on the…

Q: 8. Evaluate ze+y´+z² dV, where E is the portion of the ball centered at E the origin of radius 5, x?…

A:

Q: 5. Use spherical coordinates to evaluate the triple integral ///+y²+²dV, where E is the ball: x? +y?…

A:

Q: Evaluate the line integral ſe ry²ds, where C is three quarters of the circle a² +y? = 1, oriented…

A: C is the three quarters of the circle x2+y2=1, oriented counterclockwise. The parametric equation of…

Q: The surface area of the solid of revolution generated by rotating 3 x = (y² + 2)ž,1 sys2 about the…

A: Given function is x=13y2+332 where 1≤y≤2. The surface area of revolution of the function is given by…

Q: Find the surface area of that part of the plane 6x + 8y + z = 7 that lies inside the elliptic…

A:

Q: Suppose the divergence of the electric field in some spherical region is found to be V E = 5kr³.…

A: as given,   the divergence of electric field in some spherical region is ∇·E=5kr3 claim- to find the…

Q: 9. Using Stoke's Theorem Evaluate [(2x – y)dx – yz dy – y zdz) where c is the circle x +y =1,…

A:

Q: (b) Use Stoke's Theorem to evaluate the line integral $ (3? – 22) dr + (z² – x²) dy + (y² – x²) dz,…

A: Stokes theorem  ∮CF.dr=∫∫SCurl F .dS Where S be a smooth surface that is bounded by a  closed,…

Q: 3. Please give clear explanations

A: The parametrization of a surface S is given by       G(u, v)=(u, v, uv) where D is u2+v2≤1.

Q: Let S be a square plate with boundary C, having each side of length 2 units, lying in the plane x =…

A:

Q: (1) Compute where Cis the couater dockwise oriented boundary of upper half unit disc D.

A: It is given that, ∮Cy2dx+3xydy here C is counter clockwise oriented upper half disc D.   Here,…

Q: Evaluate the surface integral. JI (12 + y2 + 2) ds S is the part of the cylinder x2 + y2 = 9 that…

A:

Q: 63. х 3D 2t, у %3D 31, 0 <t < 3 (а) х-ахis (b) у-ахis

A:

Q: Calculate the area of the surface S. x2 y² _ z2 that lies between z = 2 and z = 6. S is the portion…

A: Explained below

Q: Find the area of the portion of the sphere x2 + y² + inder x2 + y? = 6y. %3D

A:

Q: Without evaluating the integral, show that z+4 67 -dz s 7. 2i +1 IC where C is the arc of the circle…

A:

Q: Compute the line integral Sy?a dl where y is the part of the circle centered at the origin and of…

A:

Q: Let B be the ball with center at the origin and radius 1 SIS 4(z² + y² + z*)dv = B

A:

Q: y = sec 0 tan 0 →0 TT 4 4 -Vz

A: We have given a diagram;

Q: find the surface area obtained by rotating the circle (x – 4)2 + y? =1 about the y-axis. %3D

A:

Q: For the conical surface 0 = 30°,0 <0< 21,0 <r< 2, the lateral surface area is what?

A: Sol

Q: Use Green’s Theorem to evaluate ∮C squre toot of (1 + x^2)dx + 14x dy, where C is the triangle from…

A:

Q: A conical surface is defined as 0 = 30°,0 < y< 2n,0<r< 2, the lateral surface area is what?

A:

Q: 17. Let T be the solid bounded below by the half-cone z = Vr2 + y? and above by the spherical…

A: Consider T be the solid bounded below by the half cone z=x2+y2 and above by the sphere x2+y2+z2=1.…