Let E be the solid below the plane x+y+z = 5, inside the cone V3z x² + yand in the half-space x 2 0 Set up a triple integral J J J xydV in spherical coordinates

Q: Let E be the solid bounded inside the ellipsoid = 1, where a, b and c are positive numbers. Evaluate…

A: E is the solid bounded inside the ellipsoid x2a2+y2b2+z2c2=1Where a, b, and c are positive…

Q: Evaluate the surface integral. x dS, S is the part of the plane 16x + 8y + z = 16 that lies in the…

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Q: 5. (a) Evaluate the surface integral /3² dS where o is part of the cone z = VT + y² that lies…

A: As you post multiple questions According to the guideline I only solve the first problem please post…

Q: Let E be the solid region in the first octant bounded from the sides by the cones and from above by…

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Q: Evaluate the surface integral fs F. dS where F = (4x, -2z, 2y) and S is the part of the sphere x² +…

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Q: Let S be the part of the cone z = Vx2 + y? under the plane z = 4, outside the cylinder +y 1, and in…

A: The given cone is where  The widest section of the surface is obtained at z=4, whereas the thinnest…

Q: Evaluate || f (x,y,z) dS where S is the portion of the sphere centered at the origin of radius two…

A: we have the equation of sphere x2+y2+z2=22s is the portion bounded between xy plane and z=1 in the…

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

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Q: 2. Use a parametrization to express the area of the given surface as a double integral and then…

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Q: Use cylindrical coordinates to evaluate the triple integral E Va2 + y? dV, where E is the solic 16…

A: use cylindrical coordinates of find the volume

Q: Evaluate the surface integral. dS S is the part of the sphere x2 + y² + z? = 16 that lies inside the…

A: The objective is to find the surface integral  ∫∫Sy2dS  where S is the part of the sphere…

Q: Evaluate (Vx A). ndS over the surface of intersection of the cylinders x + y a, = a which is…

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Q: Find a parametric representation for the part of the cylinder y2 + z² = 36 that lies between the…

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Q: Evaluate the surface integral. x² + y2 + z• ds S is the part of the cylinder x2 + y2 = 25 that lies…

A: Given, Where, S is the part of the cylinder x2 + y2 = 25 which lies between the planes z = 0 and z =…

Q: Let S be the part of the sphere r² + y² + z² = 4 which lies above the cone z = 3r² + 3y². Express…

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Q: Evaluate the triple integral. [l ydV where G is the solid enclosed by the plane z = y, the xy-plane,…

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Q: Evaluate the surface integral fs F. dS where F = (-2x, –5z, 5y) and S is the part of the sphere x? +…

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Q: Use Stokes' Theorem to evaluate F. dr where F(x, y, z) = xi + yj +Xx² + y² )k and C is the boundary…

A: Stokes theorem: ∮f→·dr→=∬S curl f→·n^ ds Given F(x, y, z)=xi + yj+9(x2+y2)k and C is the boundary of…

Q: Use Stokes' Theorem to evaluate | F - dr, where F (x, y, z) = zi + yj – xk and C is the 9 – z? y? in…

A: Given F→x,y,z=zi^+yj^−xk^ We have to evaluate ∫CF→⋅dr→,where C is the boundary of the part of the…

Q: dv Use spherical Coordinares to compute H 2 where W is the solid bounded by the spheres 4 ty+z² =g…

A: Given I=∫∫∫wdVx2+y2+z2Where W is the solid bounded by the spheres x2+y2+z2=9 and x2+y2+z2=4.

Q: Let Σ be part of the paraboloid z = 3 - x² – y² that lies above the xy-plane, oriented downward,…

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Q: Calculate F.dS where F = (3ry", re", z*) S is the surface of the solid bounded by the cylinder y + z…

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Q: Write the integral fS Sw ela+y²+z*)8/² dV_where W is the portion of the solid sphere a? + y? + z? <…

A: ANSWER :

Q: (b) Verify Stokes' theorem on a region which is a portion of the sphere r2 +y² +2 16 which lies…

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Q: Evaluate the surface integral || x2 z2 dS, where S is the part of the cone z2 = x² + y?, S that lies…

A: Here we solve the given problem of calculus.

Q: 4. Let f(x, y, z) = (x² + y? + z?)'/4. Evaluate II, fav = 4 centered at the where D is the solid…

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Q: Let E be the region that lies below the sphere x2+y²+z²=16, above the cone z=vx²+y² . Set up the…

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Q: Use Stokes' Theorem to evaluate F. dr, where F(x, y, z) = zi + yj – rk and C is the boundary of the…

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Q: Calculate the surface integral S FdS, where S is cylinder r² + y = 1, 0 + yz, 3 =

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Q: Consider the solid D that lies inside the cone z = and bounded by the spheres 3 y رد جر+ e][] p = 2…

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Q: 5. Use the spherical coordinates to evaluate the integral f dzdydr, where R is the region enclosed…

A: In spherical coordinates,                                       x = ρsinφsinθy= ρsinφcosθz= ρcosφ

Q: Let G be the solid which lies above the plane z = V3 and within the sphere x? + y2 + z2 = 4. Suppose…

A: we will represent the region as limit of three variable and then integrate it

Q: O Use cylindrical coordinates to evaluate the triple integral , vr + y dV, where E is the solid a by…

A: We have to evaluate the triple integral.

Q: Let G be the solid which lies above the plane z = V3 and within the sphere x² + y? + z2 = 4. Suppose…

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Q: E is the solid in R3 bounded by the cone surface z = square root (x2+ y2 ) and the plane z = 3, and…

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Q: Consider the triple integral JJJ (x+y+z)dV E where E is the solid enclosed by the cylinder x² + y² =…

A: Let's solve A and B part.

Q: Use spherical coordinates to evaluate the triple integral ∫∫∫ √(x^2 + y^2 + z^2) dv where G is the…

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Q: Let D be the solid region that lies above the cone z = x² + y² and below the sphere x+y²+= = =. The…

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Q: (a) Compute the surface integral || xy dS, where S is the quarter cylinder x? + y? = 1; x, y > 0…

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Q: Assume that S is the disk 2 + y² <4 in the plane z 0 oriented upwards with positively oriented…

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Q: Consider the solid D that lies inside the cone, and bounded below the plane, :=-4. Set up the triple…

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Q: #6. Use Stokes' Theorem to evaluate S. F dr, where F(x, y,2) = i+(x + yz)j+(xy-V) k and C is the…

A: Given that, Fx,y,z=i+x+yzj+xy-zk and C is the boundary of the part of the plane 3x+2y+z=1 in the…

Q: Consider the surface S which is the part of the cylinder x^2 + z^2 = 9 , whit   0 ≤ y ≤ 2; x ≥ 0; z…

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Q: (a) ( Evaluate the integral zdV where E is enclosed by the paraboloid z = x² + y? and the plane z =…

A: NOTE: Due to time limit only answer for (a) is given below and for (b) you need to ask in another…

Q: Consider the integral 2zx? dx dy dz, where N is the domain bounded from below by the cone z = by the…

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Q: 1. Evaluate the surface integral SL xz² ds ; o is the part of the cone z = Vx2 + y² that lies…

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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.…

Q: Use cylindrical coordinates to evaluate the triple integral /|I x² + y? dV, where E is the solid…

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Q: Let S denote the part of the cone x? + y = z² that lies between the planes z = 2 and z = 3+ x,…

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