1- Calculate the surface integral [fs G(r)dA, where G = (1+½xz)} and 5 is given by the parametrization r(u, v) = [u, v, 2u³], 0

Q: Evaluate the unoriented line integral (22 + y° + z²) ds (2x² along the parametric curve a : [0, 1]…

A:

Q: Use Green's Theorem to evaluate the line integral v+e*) dx + (6x+cosy) dy where C is the triangle…

A:

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 line integral f e-*(cos y dx - sin y dy), where c is the rectangle with vertices (0,0),…

A: The line integral function is ∫Ce-xcosydx-sinydy. The vertices of the rectangle is 0, 0, π, 0, π,…

Q: .Find the exact value of the double integral. J (2x + 5y) dA, where R is the rectangular region…

A:

Q: Use Green's Theorem to calculate the work done by the force F on a particle that is moving…

A:

Q: Evaluate the triple integral ∫∫∫T (x^2) dV where T is the tetrahedron with vertices (0, 0, 0), (1,…

A:

Q: According to the divergence theorem, one of the following integrals represents the surface integral…

A:

Q: 7. Evaluate the line integral f, F· dr where F(x,y, z) = x³i – y²j+ zk and C is the x2 + 2xy + y²…

A:

Q: Calculate the integral I = = • (y² + z²) dx + (z² + x²) dy + (x² + y²) dz where I is the…

A:

Q: Evaluate the triple integral. I/| (x - y) dv, where E is enclosed by the surfaces z = x2 - 1, z = 1…

A:

Q: 10. Use Green's Theorem to evaluate the line integral (e" - y) dx + x cos(y²) dy, where C is the…

A: 1/2 + ( (1/2 )sin 1)

Q: Evaluate the surface integral. z + x2y x²y) ds S is the part of the cylinder y² + z2 = 9 that lies…

A: We have to find the surface integral from the given condition

Q: Evaluate the triple integral. 16.  ∫∫∫T  xz dV , where T is the solid tetrahedron with vertices…

A: The solid tetrahedron T with vertices 0, 0, 0, (1, 0, 1), (0, 1 ,1) and 0,0, 1. The solid region is…

Q: 1- Calculate the surface integral ffs G(r)dA, where G = (1+ æz) and S is given by the…

A:

Q: 15- Evaluate the surface integral f, xy dswhere x is the part of the plaue y = 1-x-z that lies in…

A:

Q: Evaluate the line integral I of the one-form w = xy dx + 12y dy over the parametric curve a : [0,…

A: Given: ω=xydx+12ydy To find: I=∫αω  where α:[0,ln2]→ℝ2 with α(t)=(e2t,e-2t) ∴x=e2t,y=e-2t Now,…

Q: 3 Use polar coordinates to evaluate the integral (3) f[/x² +y° dA Ris bounded by the semicircle y =…

A:

Q: (1) (i) Use the Divergence Theorem to calculate the surface integral /| F- dS, that is, calculate…

A:

Q: Calculate the surface integral ∫ ∫ s F ∙ N dS where F (x, y, z) = -y2i + xj + k and S is the shaded…

A: We will find out the required surface Integral.

Q: Evaluate the triple integral // x dV, where T is the solid tetrahedron with vertices T (0,0, 0),…

A: Here we have to evaluate the triple integral , where T is the solid tetrahedron with vertices…

Q: 1. Use the Divergence Theorem to evaluate /| F.dš where F.dSv F = yx? i+ (xy? - 324) j+ (x³ + y?) k…

A:

Q: 1- Calculate the surface integral Sl,G(r)dA, where G = (1+%rz)ź and S is given by the…

A:

Q: Use Green's Theorem to evaluate the line integral S(x² + y²)dx + (x² – y²) dy where C is the…

A:

Q: Evaluate the flux integral F-ds where Pis the part of the paraboloid -= 4-x -y above the xy plane…

A: Any integral which is to be evaluated at the surface is called the surface integral. Divergence…

Q: 387. Use the divergence theorem to calculate surface integral F. dS when F(x, y, z) = x²z³i+ 2xyz³j+…

A: Given that: F(x,y,z)=x2z3i+2xyz3j+xz4k and S is the surface of the box with vertices (±1,±2,±3).

Q: 2- Use Gauss's divergence theorem to evaluate the surface integral / ry dydz + 2y°dxdz + y?zdxdy),…

A:

Q: 16. Use the Divergence Theorem to find the outward flux across the boundary of the region D where F…

A:

Q: Use either form of Green's Theorem to evaluate the following line integral. $9x²1² 6 C $9x³y² dx +…

A:

Q: Evaluate the triple integral ∭E(x+2y)dV where E is bounded by the parabolic cylinder y=2x2 and the…

A:

Q: 1. Use a parametrization to express the area of the given surface as a double integral and then…

A: Here we will cylindrical co ordinate system to parametrize the surface  x=r cosθ , y = r sinθ , z=z

Q: 3. Evaluate /// 2* dV if G is a solid in the first octant bounded by the plane y + z = 2 and the…

A: triple integral

Q: (1) Evaluate the triple integral I zyz dV, R where R = {(z, y, z)| 0 < z < 3, -2 <y< 1, 1< z < 3}.

A: We will use simple Integration rules to solve this triple integral.

Q: (b) Evaluate the surface integral S.S x² dS over the surface x² + y² = 1 between z = 1 and z = 4.

A: x=cos(u), y=sin(u), z=v  0≤u≤2π, 1≤v≤4 S(u,v)=&lt; cos(u), sin(u), v &gt;

Q: 9. Evaluate the line integral of F = (2xy + 1,x² + 2yz, y? – 2) over the region C parametrized by…

A:

Q: Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise. y10 dx + x6…

A:

Q: Use Green's Theorem to evaluate the line integral Lv+e) dx + (3x+cosy) dy where C is the triangle…

A:

Q: Evaluate the triple integral. SSS 5x²e" dv I where E is bounded by the parabolic cylinder z = 1 - y²…

A:

Q: Evaluate the triple integral II. x* dV, where T' is the solid tetrahedron h vertices (0, 0, 0),…

A:

Q: 3.4.6 Use Green's theorem in a plane to evaluate of 10x9²³- [(xy²-y) dx + (x + y²) dy] C as a double…

A:

Q: (b) Let F(x,y) = (e2*y+cos(7x²), xºy^+e>Y³} Use Green's Theorem to set up the line integral F. dr as…

A:

Q: I have trouble getting to the answer. Just wondering if I can get it step by step.

A: Consider the region for solid.Let the solid be bounded by the coordinate planes and the plane 2x +…

Q: (1) Evaluate the double integral L V² + y² +1 dA where D is a quarter disk of center O(0,0) and of…

A:

Q: 7. Use Green's Theorem to compute the line integral | ry? dx – x² dy, where C is the triangle with…

A: ∫xy2dx - x2dy triangle vertices are (0,0), (2,0), and (2,2)

Q: Evaluate the triple integral -p (x + 6y) dV where E is bounded by the parabolic cylinder y = 8x² and…

A:

Q: Evaluate the line integral: f y² dx + x² dy by parameterizing C where the curve C is a square R with…

A: According to the given information, it is required to evaluate the line integral.

Q: 1. Evaluate the following surface integrals: (a) (x + y) dS, 0 : part of the surface 2x + 3y + z = 6…

A:

Q: Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise. e5x + 2y dx +…

A:

Q: Evaluste the line integral using Green's Theorem and check the answer by evaluating it directly.…

A:

Q: 3. Evaluate the triple integral || ryz dV; G is the solid in the first octant that is bounded by the…

A: To evaluate the given integral ∫∫∫Gxyz dV. The limits are given as  z=0 to z=2-x2 and y=0 to y=x and…