1. A ship conveys goods from port A with position vector d= i -j-k to port B with position vector b= 2i +j+ k. Using your knowledge of line integrals, caleulate the total work done by the ship if the force that propels the ship is F (1. v.:) - (v cos(:) + 2re") i+ (2ry cos(:) + sin k

Q: 5. Verify Green's Theorem for 0(xy +x )dx+(4x-1) dy where Cis shown below by (a) computing the line…

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Q: Evaluate (₁ F. dr using the Fundamental Theorem of Line Integrals. Use a computer algebra system to…

A: NOTE: Refresh your page if you can't see any equations. . C:=smooth curve form (-5,4) to (3,2)…

Q: Set up an iterated triple integral equal to √3-1² 2²+² 3 I = 1-[²√²² ² 2-√√4-x²-y² using 1.…

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

Q: Find the solution in the form of Fourier integrals: Ut- 3uxx = 0, u(0, t) = 0, |u(x, t) bounded as x…

A: As per the question we are given a initial boundary value problem as : ut - 3uxx = 0 And we have to…

Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

A: Given:

Q: Show that the line integral is independent of path, and use the Fundamental Theorem for line…

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Q: 1 3 he integral I | f(x, y)dydx. 3x on and change the order of integra

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Q: Evaluate the line integral §. xy²dx + 2x²y dy over triangular path with vertices (0,0). (2,2) and…

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Q: 19. Find. thedivergen ce. and.cur..4the fellowiny vecter. field: a.. F = Xej+. y.e... b. Ês ĕsiny i…

A: We need to find the divergence and curl of the following vector fields. a. F→=xeyj+yezk=(0,xey,yez)…

Q: The plane figure below is a square of side length 2 with a quarter circle of radius 1 taken out of…

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Q: Find the solution in the form of Fourier integrals: U4-3uzz = 0, |u(x, t) bounded as x → ±0, sin r…

A: We are given the following second order partial differential equation : ut - 3uxx = 0  ;  -∞ < x…

Q: Evaluate the line integral J xe" dx +y sin y dy along the triangular path consisting of the line…

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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: [[(2x + y²) da + 2xy dy], where C is the line segment from (-1,0) to (1, 2) Evaluate in two…

A: The line integral ∫CMdx+Ndy involves the integration over a specific path. In this case, the line…

Q: Find the moment of inertia about the​ x-axis of a thin plate bounded by the parabola x=2y-3y2 and…

A: Given that the equation of the parabola,x = 2y – 3y2and the equation of linex + 7y = 0

Q: 3) S. (3x² – 3yz + 2xz)dx + (3y² – 3xz + z²)dy + (3z² – 3xy + x² + 2yz)dz - Calculate the…

A: Let's find.

Q: 3. Evaluate the indicated line integrals in the complex plane by direct integration. Siz dz along…

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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 §. xy²dx + 2x²y dy over triangular path with vertices (0,0), (2,2) and…

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Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

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Q: Evaluate the integral / (10x + 15y)dx + (18x – y)dy along the paraboli - arc y = x² from (0,0) to…

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Q: Evaulate the line integral of c (x^2+y^2) where c is the line segment from (-1,-1) to (2,2)

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Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

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Q: Evaluate the following line integrals in the complex plane by direct integration (not using…

A: Complex

Q: 8. Verify Green's Theorem for + (6y – 3y +z) dz + yx°dy where C is shown below by (a) computing the…

A: Let F=Px,yi+Qx,yj be the vector field and C be the boundary of the region D. The Green's theorem…

Q: 3. Compute the line integral of F(x, y) consisting of the line segment from (T,0) to (2, 5),…

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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: Verify that the Fundamental Theorem for line integrals can be used to evaluate the following line…

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Q: 7. Verify Green's Theorem for O (6 +2) dz + (1 – 2ry) dy where C is shown below by (a) computing the…

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Q: Find the solution in the form of Fourier integrals: U₁-3 = 0, uz (0, t) = 0, |u(x, t) bounded as…

A: We have the following partial differential equation : ut - 3uxx = 0  , x,t > 0 With boundary…

Q: 3) . (3x2 — Зуz+ 2xz)dx + (3у? - 3xz + z?)dy + (372 — Зху + х? + 2yz)dz Calculate the curvilinear…

A: Let's find.

Q: How do I set up the triple integral of the function xy2 -3z, where the solid is bounded by the…

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Q: Set up an iterated triple integral equal to 3 3-x² x²+y² 3 2-√4-x²-y² using: Spherical coordinates…

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Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

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Q: 2. Evaluate O (2y + In(5x² +3)) dx + (10x 3) dy along the boundary of the elliptic- region 4. y? 1…

A: Introduction: Green's theorem is very efficient in calculating line integral. When the line intgeral…

Q: 8.) Find work done by F = (2x³y* + x, 2x*y³ + y) along the path r(t) = (t cos(at) – 1, sin (t))…

A: Since we have given that F = 2 x3 y4 +x, 2 x4 y3 +y   and rt=t cosπt-1, sinπ2t    drt = cosπt -t…

Q: Evaluate the line integralſ (x + 2y) dx + x² dy, where C consists of line segments from (0,0) to (2,…

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Q: 8. Verify Green's Theorem for (6y – 3y? +x) dx + yx*dy where C is shown below by (a) computing the…

A: Given integral is ∮C6y-3y2+xdx+yx3dy Here C consists of two line,  C1:Line joining 0,0 and…

Q: Evaluate the indicated line integrals in the complex plane by direct integration. Siz dz along the…

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Q: Integrate f(z) = 1 counterclockwise around the unit circle, using 28 – 4.4 Cauchy's integral theorem…

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Q: 3) S. (3x² – 3yz + 2xz)dx + (3y² – 3xz + z²)dy + (3z² – 3xy + x² + 2yz)dz Calculate the curvilinear…

A: Let's find.

Q: C3x-3y2 +2x2) dxt (3y-3x2+2²)dy (3²-3xytx*2yz)da calculate the curvilinear integral.where cis any…

A: Let's find.

Q: Evaluate the line integral (4х + 5у)dx + (За — 6у)dy along the - curve C : x = 10 cos t, y = 20 sin…

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Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

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Q: Calculate the line integral of F(x, y) = -4i + 5j along the line segment from (-3,-4) to (-5,0).…

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Q: Find the line integral of C in two ways; A) Directly. B) Using Green's theorem. C eata formed by the…

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Q: Verify that the Fundamental Theorem for line integrals can be used to evaluate the following line…

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Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

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Q: 2. We have seen that the FTC for line integrals implies fc Vf - dĩ = 0 for any smooth closed path C…

A: FTC for line integrals implies ∫C∇f·dr→=0 for any smooth closed path C and any smooth function f (a)…