Evaluate the integral // Fn ds where F = (2r+32)i-(rz+y)3+(y² +2)& and S is the surface of the sphere having center (3, -1,2) and radius 2.

Q: Find the line integral of F(x, y) = (x²– y², 2.xy) = (P, Q) along the boundary of the rectangle [0,…

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Q: Compute the double integral R ye®Y dA where Ris the square -1 < x < 1, 0 < y< 2.

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Q: Calculate the double integral. 4x dA, R = [0, 4] × [0, 1] 1 + xy

A: The given integral is ∬R 4x1+xy dA  where R=0,4×0,1. Evaluate as follows.

Q: Calculate the integral f, (3y – 3x²) dæ + (9x) dy where y= aD is the counter-clockwise boundary of…

A: we are allow to solve one question at a time thank you

Q: The double integral I = S," S* Jx² + y² dydx in polar coordintes is:

A: In polar coordinates,  x=rcosθ, y=rsinθ, dydx=rdrdθ

Q: 'ind the line integral of F(x, y) = (x² – y² , 2xy) = (P, Q) along the boundary of the rectangle %3D…

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Q: Evaluate the line integral [21r²yzds with respect to s along the 2 curve C : x = t₁ y = t², z =…

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Q: Evaluate the line integral by two methods: (a) directly and (b) using Green’s Theorem.3. ∮C xy dx +…

A: According to Greens theorem :

Q: Set up an iterated triple integral equal to | = √√3 √3-x² √√30 x²+y² 3 √2-√4-x²-y² 2y dz dy dx…

A: The given problem is to set the given triple integral in Cartesian coordinates to convert into the…

Q: Find the line integral of F(x, y, z) = x³i + yj+ zk along th the origin to the point (3, 2, 6). F.…

A: See the details solution in below

Q: + y^5)dy] where C is the unit circle x^2 + y^2 = 1 traversed counterclockwise.

A: we have to compute the given integral ∮x5+y3dx-(x3+y5)dy     where C is unit circle x2+y2=1.C

Q: 2. Use Green's theorem in order to compute the line integral P (x – 4)³ dy – y³ dx where is the…

A: We need to compute the given integral using Green's theorem . ∮C(x-4)3dy-y3dx Where is the circle of…

Q: Use Green's Theorem to calculate line integral o sin(x²) dx + (3x – y) dy where C is a right…

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Q: Set up an iterated triple integral equal to √√3 S√ SO 3-x² x²+y² 3 2- 4-x²-y² using: a. Cylindrical…

A: Since you have posted multiple questions, we will solve the first question for you. If you want any…

Q: Use Green's theorem to find the line integral of 2x dx – 7x2 dy counterclockwise around the triangle…

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Q: Evaluate the line integral (direct method) | (3x– y) dx – x dy , where C consist of the parabola…

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Q: Solve the integral. + yz )do; o: part of the plane x + y +== 6 that lies in the first octanct.

A: Solution:

Q: . Calculate the flux integral fF.n ds, where C is the positively oriented circle of radius 1…

A: Given function is, Fx,y=x,2y The formula for calculating the flux of the integral ∮F·nds is,…

Q: 1 (x²+y*) dx dly -1 2

A: Consider ∫-11∫24(x2+y2) dx dy = ∫-11x33+xy224 dy = ∫-11643+4y2-83-2y2dy = ∫-11563+2y2dy =…

Q: Suppose f(x, y, z) = x² + y² + z? and W is the solid cylinder with height 9 and base radius 5 that…

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Q: Sketch the curve ĕ= E Set uf, buz de not evaluale, an integral for the are- length of the Rurve from…

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Q: Evaluate the line integral (direct method) |(3x– y) dx – x dy , where C consist of the parabola y=…

A: Given integral is, ∫C(3x-y)dx-xdy

Q: Evaluate the line integral |-ydx + xdy along the curve C : y² = 24x from (24, 24) to (0, 0).

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Q: Use Green's theorem in order to compute the line integral (2sin z + 3y²) dx + (sin(4®) + 2x³) dy…

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Q: Evaluate the line integral C:y² = 30x from (30,30) to (0,0). NOTE: Enter the exact answer. [-ydr +…

A: line integral

Q: Evaluate the line integral F. dr, vhere F(z, y) = -yi-rj and C is the curve y = v4-a from (2,0) to…

A: We have to find the line integral

Q: Evaluate the triple integral, 2xy dV, where the intergral is bounded by the parabolic cylinders y =…

A: The given triple integral,

Q: Use Green's theorem to evaluate the line integral along the given positively oriented curve. [(5y +…

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Q: S. (3x² – 3yz + 2xz)dx + (3y² – 3xz + z?)dy + (3z² – 3xy + x² + 2yz)dz

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Q: Evaluate the line integral ∫(AB) xdx+ydy+zdz using the fact that the integrand is a perfect…

A: Here we find ∫(AB) xdx+ydy+zdz,   by using the fact that the integrand is a perfect differential. A…

Q: Use spherical coordinates to evaluate the integral •√₁-x² √√₁-x²-x² (x² + y² + ²)dzdydx.

A: To evaluate the integral using spherical co-ordinate system :-

Q: Set up an iterated triple integral equal to - TV³√ SO √√3 | = √3-x² x²+y² 3 2-√√4-x²-y² using: a.…

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Q: Use Green's theorem to evaluate the line integral along the given positively oriented curve. | 6y3…

A: given circle x2+y2=4

Q: Evaluate the triple integral x dV where G is the solid that lies below the surface z = 15xy and G.…

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Q: Compute the integral |(5y + pz2020, ) dx + (19x – e-4ycos(v) sin y) dy over the portion of the…

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Q: Express the double integral || (x +1)dA, where 2 is the region in the upper half- plane (i.e. y20)…

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Q: Evaluate the iterated integral LL V-6x-x2 ху (x2 + y2)3/2 dydx -3 J0 using polar coordinates.

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Q: Evaluate the triple integral. 8x dV, where E is bounded by the paraboloid x = 2y2 + 2z2 and the…

A: The objective is to evaluate the triple integral ∫∫∫E8xdV, where E is bounded by the paraboloid…

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: 2. Compute the scalar line integral xy ds where C is the part of the circle of radius 2, centered at…

A: Put x=2cost , y=2sint

Q: Evaluate the triple integral x dV where E is the solid bounded by the paraboloid x = 6y² + 6z² and x…

A: To evaluate the triple integral ∬∫ExdV where E is the solid bounded by the paraboloid…

Q: Given the scalar functionf (x, y) = 2xy, calculate the line integral along the ellipse curve+ 1 from…

A: Given: f(x,y)=2xy From the point (3,0) hesta (0,2)

Q: 2+ y²) dz dy

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Q: Evaluate the triple integral. 10x dv, where E is bounded by the paraboloid x = 2y² + 2z2 and the…

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Q: dl /x² + y² + 4

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Q: Evaluate the contour integrals cosh z dz 4z2 + 72 z +1 dz 223 – 322 – 2z and around the unit circle…

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Q: Use Green's theorem to evaluate the line integral along the given positively oriented curve. 3y +…

A: We have to solve the given problem by Green's theorem.

Q: Set up an iterated double integral in polar coordinates equivalent to the area of the surface on the…

A: You asked for the surface below z=2, not bounded below by plane z=2,

Q: Use Green's Theorem to evaluate the line integral along the gi | 4y3 dx - 4x³ dy Cis the circle x2 +…

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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. 2y3 dx…

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