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Q: Evaluate the line integral where Cis the intersection of the cylinder * +y' =1 and the plane…

A: evaluate the line integral ∫C-y3i+x3j-z3k dr where C is the intersection of the cylinder x2+y2=1 and…

Q: Use Green's Theorem to evaluate the line integral of F = (r°, 4z) around the boundary of the…

A: In the given question, concept of Green Theorem is applied. Green Theorem Green's theorem is most…

Q: 386. Use the divergence theorem to calculate surface integral F-dS, where F(x, Y, z) = xªi – a³z²j+…

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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. Ex + 9…

A: According to the given information it is required to evaluate the integral using green’s theorem.

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

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Q: Q3// A surface S is defined by 2x2 + z = 1 and the bounded by the planes y = 0,y 2, x 0,z = 0 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: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise p…

A: As we know that; The Green's theorem; ∫CPdx+Qdy=∫∫D∂Q∂x-∂P∂ydA   Given: I=∫C3xy dx+6xy dy And C:…

Q: 3 Let S be a square plate with boundary C having length of each side as 2 units and lying in the…

A: The plane is given as y = 1, so plane S is y = 1   The unit normal vector to the surface S is:

Q: valuate Hhe lime initeqratl v¢•dr, where x,4,)= 2xy+ 3x2, m tuo different ways. A: Use 7(6) - for…

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

A: To evaluate the below line integral. ∮C5y2dx+3x2dy

Q: 52. Show that a spherical cap of height h and radius R (Figure 19) has surface area 2n Rh. Rogawski…

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Q: Use Stockes' theorem to calculate the line integral fc F · dr where F (1,4) = (3zy + eN i + (25° –…

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Q: a change of uaria bles to evaluate X-24 dA where R.isthe use the integralS, 3x-Y R Parallelogram.…

A: Given integral is ∬Rx-2y3x-ydA where R is the parallelogram enclosed by x-2y=0, x-2y=4, 3x-y=1and…

Q: the integral that calculates the area of the region enclosed by the circle 3/3 in the upper half…

A: To calculate- Area of the region enclosed.

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

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Q: Q#5. Evaluate the surface integral When f(x, y, z) = 3xyz and g is the portion of the plane × + 3y +…

A: We have to find Surface integral  f(x,y,z) = 3xyz Plane given is x+3y+5z = 6 in first octant

Q: Each of Exercises 29–32 gives an integral over a region in a Cartesian coordinate plane. Sketch the…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise. $…

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Q: 2/ MATH

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Q: Evaluate the integral 1 dz. Lancon z(272 + 3)²(z+ + 2)³ Hint: Use the parametrization y:[-T, T] → C…

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Q: Collatate the thiple integrals: SSS z dv E where is the domain banded by the parabol = = 3(x² ty²)…

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Q: 3. Evaluate xyz dS, where S is the part of the plane z = 6- y that lies in the cylinder x +y? = 4.

A: To Evaluate: ∬Sxyz dS, whereS is the part of the plane z=6-y that lies in the cylinder x2+y2=4.…

Q: Calculate the line integral fe F. dr, where F = (ry, r? + y? + 22, yz), and C is the boundary of the…

A: Step:-1 Given that a parallelogram with vertices 0, 0, 1, 0, 1, 0, 2, 0, -1, 2, 1, -2 and F→=xy,…

Q: y*dx + x*dy = (N, – M,) • dA (м, - м,) ал

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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: Jse Green's Theorem to evaluate the line integral along the positively oriented closed curve C.…

A: The equation of a straight line joining two points x1, y1 and x2, y2 is given by the formula: y-y1 =…

Q: O Given Fley,e)= Use the parametric descriphion CiP(H = , oŚ€€ to directly evalvate the line…

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Q: Use Štoke's Theorem to evaluate the line integral - 2ydx +-6zdy + dz where C is the intersect | of…

A: Strokes theorem is ∫CF→.dr→=∫∫S∇×F→.N→dS=∫∫ScurlF→.N→dS x=rcosφy=rsinφ

Q: Let F(r, y, z) = r²i+ y²j+ z²k and S the surface of the region bounded by 5. the cylinder 1? + y² =…

A: Divergence theorem

Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise. 2…

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise. p…

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

A: Given ,x2+y2+z2 = 22       _________(I)and z = x2+y2     __________(II)Putting the value of z from…

Q: a) Evaluate ||| x²yz dV, where G is solid in the first octant that is bounded by parabolic cylinder…

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Q: Express the surface integral as an iterated double integral by using a projection of S on the…

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Q: Use a line integral to find the area of the surface that extends upward from the parabola y = x² (0…

A: We have to use a line integral to find the area of the surface that extends upward from the parabola…

Q: |Evaluate the line integral: f.(r² + y) dx + (4x – cos(y)) dy where C is the boundary of the square…

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Q: 6. Evaluate the surface integral where o is the portion of the cone z = Vr? + y? between the planes…

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Q: Use Stockes' theorem to calculate the line integral fe F.dr where F (2.52) = (szy + e)i + (2 – Iny)3…

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Q: 3. Evaluate the surface integral , F·n dA by the divergence theorem. Shoe details F = [ siny, cosx,…

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise. O…

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Q: 2. Suppose that S is a surface in R3 with unit normal vector N surface area of S is given by (n1,…

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise.…

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Q: 5) Using Green's theorem, convert the line integral .(6y? dx + 2xdy) to a double integral, where C…

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise. p…

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Q: 5) Using the de finition of the contour integral conmpuute the integral of f 12)= 1+i-2ž from Zo =0…

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise. O…

A: Integral given is- ∮C3xydx+4xydy,  Where C is oriented counterclockwise and is the rectangle bounded…

Q: The wedge cut from the cylinder, x? + y² = 1 by the planes, z = -y and z = 0. Use a tripple integral…

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