Compute the work done by the force field F =< x² + 2y, 4x + y° where C is the boundary of the region bounded by y = sin x %3D y = 0 x = 0 X = T and traverses counter-clockwise.

Q: Compute the line integral of the scalar function f(x, y) = /1+9xy over the curve y = x³ for 0 < x <…

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Q: Compute the line integral of the scalar function f(z,y, 2) = 2z² + 8z over the curve c(t) = (e*, t²,…

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Q: Evaluate the line integral I of the one-form w = (y+ z) dx + (x + z) dy + 10z dz over the line…

A: We have to find the line integral.

Q: Find the work done by the force F(x,y, z) = x*j + 5zk over the curve C: r(t) = cos t i+ sintj+ tk,…

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Q: Find the flux F(x, y, z) = (xy²,x²y, ln(x + y)) directed outwards through the surface of the solid…

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Q: Verify Stokes's Theorem by evaluating F.dr as a line integral and as a double integral. F(x, y, z)…

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Q: Exercise 10.6 Evaluate the line integral using a method of your choice. e¯*(cos y dx + sin y dy),…

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Q: 11. Find the F in the surface S integration ffrnd where n is the normal unit vector to the S F=xi+zk…

A: Given F=xi+zkS : 2x+y-2z=6  where x≥0, y≥0, z≤0

Q: Evaluate the line integral by applying Green's theorem. 7xy dx + (x + y) dy, where C is the boundary…

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Q: Calculate the line integral [(of).do where f(x, y, z) = x ² ¹² + 4 xy² z yz с + е хуча and C is the…

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Q: compute the line integral f(x, y) ds for the given function and path or curve. f(x, y) = x – y, the…

A: Given: fx,y=x-y To Find: Line integral ∫Cfx,yds over the unit semi-circle x2+y2=1, y≥0

Q: Compute the line integral of the scalar function f(x, y, z) = 2x² + 8z over the curve c(t) = (e',…

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Q: By using two methods, find the work done by the force field F(x, y) = ysin xỉ + xe³ ĵ to move a…

A: Given: To compute:  ∫C F.dr=?F→(x,y ) = y sin x i^…

Q: Compute the line integral of the scalar function f(x, y) = /1 + 9xy over the curve y = x' for 0 < x…

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Q: Compute (VxF). dS, where S is given by x² + y² + (z − 1)² = 2 and z ≥ 0, F(x, y, z) = (-esinzy, x +…

A: The general form of a vector-valued function is given by F1,F2,F3 where F1,F2 and F3 are the scalar…

Q: Evaluate the line integral | F•ds where F = 2xyi + (x – y²)j and C is (a) y = x from (0,0) to (1,1)…

A: For the solution follow the next steps.

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

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Q: Calculate the value of the line integral fds where f(x, y, z)=e² and C is described by X C (x, y,…

A: The objective of the question is evaluate the definite integral.

Q: Compute the line integral of the scalar function f(x, y) = over the curve y = x° for 0 <x <1 /1+ 9xy…

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Q: Evaluate the line integral ex dx - xy dy +y dz, where c(t) = (1, t, t ), 0 sts 1. %3D

A: As per our guideline we are supposed to answer only first asked question.Kindly repost other…

Q: Calculate the double integral. ∫∫ x sec2y dA, R = {(x,y)| 0≤ x ≤2, 0≤ y ≤ π/4 }

A: Given: The given function is  f(x,y)=x sec2(y) and the region is R=(x,y)|0≤x≤2 , 0≤y≤π4  To find: we…

Q: A uniform electric field points in the :-direction, E = Ek. By explicitly calculating the surface…

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Q: Compute the line integral of the scalar function f(x, y) = /1+ 9ry over the curve y = x° for 0 <¤ <…

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Q: Find the flow of the velocity field F = (y + z)i + xj - yk, where velocity is measured in meters per…

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Q: Verify Stokes's Theorem by evaluating F(x, y, z) = xyzi + yj + zk S: 8x + 8y + z = 16, first octant…

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Q: Calculate the flux integral. ∫S(2i+zk )dA where S is z=x^2+y^2 with 0≤x≤1, 0≤y≤2 oriented upward.

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Q: Evaluate the surface integral /F- ds for the veetor field F = (y. -r, 2:), where S is the hemisphere…

A: Surface integration

Q: Evaluate the given integral by using a transformation to cylindrical coordinates: f (x2+2)¹/2 dv,…

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

Q: Consider out counterclockwise. fo x²y dx - xy² dy, where C is the boundary of the region 0 ≤ y ≤ √√4…

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Q: Verify Stokes's Theorem by evaluating F. dr as a line integral and as a double integral. F(x, y, 2)…

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Q: Calculate the double integral f SR T cos(2a + y) dA where R is the region: 0 <I<0 <y

A: To find- Calculate the double integral ∬Rx cos2x + y dA where R is the region: 0 ≤ x ≤ π6, 0 ≤ y ≤…

Q: aluate the line integral fc F dr, where F(x, y, z) =3 sin xi + 2 cos yj+ 4xzk and C is given by the…

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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: Evaluate the line integral F. dr, where F(x, Y, z) = –xi yj – 5zk and C is given by the vector…

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Q: Evaluate the line integral | F•ds where F = 2xyi +(x – y²)j and C is (a) y=x from (0,0) to (1,1) (b)…

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

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Q: Evaluate the line integral f F · dr, where F(x, y, z) = –2xi + 3yj + 3zk and C is given by the vecte…

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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: Calculate the line integral of h (x, y)= (2ŋ) i +(x - 2y)j. over r (u) = cos ui+ sin u j, u €…

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Q: Use Stokes' theorem to evaluate line integral (z dx + x dy + y dz), where C is a triangle with…

A: Consider the provided question, We have to evaluate the given integral by using the stokes theorem,…

Q: Evaluate the given circulation integral on the closed curve C below. $ (x² + y²) dx – 2æydy (1, 1) y…

A: From the given problem:   I=∫cx2+y2dx-2xydy   Fro the Stoke's theorem:   ∮F→.dr→=∬curlF→n^ds   It…

Q: Evaluate the following line integral I=[3x°dx + 2yzdy +y°dz from A: (0, 0, 0) to B: (2, 4, 8) a) By…

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Q: . Integrate f(x, y) = cos (x² + y²) (a) over the closed unit disk; (b) over the annular region 1 <…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Compute the line integral (yze"y= + y² + z – 2x) dx + (xze"v² + 2xy) dy + (xye"y= +x+ 3z²) dz C…

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Q: Evaluate the line integral F dr, where C is given by r(t) = (t², t, vT), 0<ts2 and (x, y, z) = (z,…

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Q: find the outward flux of F across the boundary of D. F = (6x + y)i - (x + z)j + 4yz k D: The region…

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Q: A) if F=2yi-zj+xk evaluate line integral Fxdr along the curve x=cost,y=sint,z=2cost from t=0 to…

A: Given x = costy = sintz = 2cost As F = 2yi-zj+xk Then F(x,y,z) = 2y , -z , x Thus F(x(t) , y(t) ,…

Q: Compute the line integral [(yze²v² + y² + 2 − 2x) dx + (xze²v² + 2xy) dy + (xye²³² +x+32²) dz, where…

A: We have to compute the line integral ∫Cyzexyz+y2+z−2xdx+xzexyz+2xydy+xyexyz+x+3z2dz, where C is the…

Q: A. Evaluate and sketch the line integral :1 = f yx dx + (2X – Y)dy around the region bounded by…

A: Greens theorem

Q: Verify Stokes's Theorem by evaluating S F(x, y, z) = (-y + z)i + (x − z)j + (x − y)k S: z = √1-x² -…

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