Compute the line integral of the scalar function f(z,y, 2) = 2z² + 8z over the curve c(t) = (e*, t², t), 0

Q: Use Green's theorem to evaluate the line integral along the given positively oriented curve. ye* dx…

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Q: 1. Calculate the line integral f F-d7, where F (z. y, 2) = -y? +z3 +zk and C is the path C along the…

A: This is a problem from line integral.

Q: Evaluate the double line integral S  of the fuinction (x − 2y + z) dS. S: z = 9 − x,  0 ≤ x ≤ 9,  0…

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Q: 5z dv, where E is bounded by the cylinder y2 + z2 = 9 and the planes x = 0, y = 3x, and z = 0 in the…

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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. | yex…

A: To evaluate the given line integral along the given positively oriented curve. ∫Cyexdx+2exdy Where C…

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

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

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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. xy2 dx…

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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: Evaluate the line integral / V(ry + xz + yz) · dĩ over the curve F(t) = (t, 2t, 3t) for 0 <t < 4…

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Q: Evaluate the line integral f. (2x – 4xy)dx + 3xy – 2x³y)dy over the straight path L joining point…

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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: Compute the line integral of the scalar function f(x,y,z)=2x2+8zf(x,y,z)=2x^2+8z over the curve…

A: To find the line integral, obtain dS as follows.

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

A: Let's find.

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

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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: 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: Calculate the line integral F(x, y, z)=2xy^2 i+(2yx^2 +2y)j     on a path from (0, 0, 0) to(3, 1, 1)

A: We need to compute the line integral: F(x,y,z)=2xy2i+(2yx2+2y)j on a path from the point: 0, 0, 0 to…

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

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

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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: Evaluate the triple integral. 4x dV, where E is bounded by the paraboloid x = 5y2 + 5z2 and the…

A: We have a paraboloid, and each cross section is a circle, parallel to the plane x = 5. We use…

Q: Evaluate the triple integral. 7x dV, where E is bounded by the paraboloid x = 5y2 + 5z2 and the…

A: Here, E is the surface boiunded by the  paraboloid x=5y2+5z2 and the plane x=5. Now, at x=5,…

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: Find the line integral of F = 2√√zi-4xj + 3√yk, from (0,0,0) to (1,1,1) over each of the following…

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Q: 2) Show that the integral f. (cosyz dx – xz sinyz dy - xy sinyz dz) is path independent and find its…

A: Condition for line integral to be path independent is given below. ∫cFdr is path independent if F…

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: (a) Find the line integral of f (x, y, z) = -x + y + z over the straight-line %3D segment from (1,…

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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: Find the line integral of F= 2√zi-4xj + 3√√yk, from (0,0,0) to (1,1,1) over each of the following…

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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 I of the one-form w = (y + z) dx + (x + 2) dy + 10z dz over the line…

A: Given: One-form ω=y+zdx+x+zdy+10zdz and the line segment joining 0, 0, 0 and (3, 1, 0). To find:…

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

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Q: 2) Find the outward flux of F across the region D where F(x, y, z) = (In(x² + y²), –tan'(), zVx² +…

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Q: Determine the line integral of the differential form (x + 3y²)dx – (-6xy + z)dy from points (1,0,3)…

A: Let us consider the Curve C which is parameterized by r(t)=(x(t),y(t),z(t)), a≤t≤b ∫CP dx+Q dy…

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: Compute the line integral of the scalar function f(x,y,z)=2x2 +8z over the curve…

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Q: Use Green's theorem to evaluate the line integral F•ds where F = 2xyi +(x-y')j and C is the %3D path…

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

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Q: (6) Evaluate the line integral / r²ydx + xy°dy, where C is the square with vertices (0,0), (1,0),…

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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: Use Green's theorem to evaluate the line integral [F•dš where = 2xyi +(x- y')j and C is the path…

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Q: The line integral (x+/y) ds , where C is the line segment joining the points (0, 0) and (1, 1) , can…

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Q: Compute the line integral of the scalar function ƒ(x, y, z) = 2x² + 8z over the curve c(t) = (e¹,…

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Q: dl /x² + y² + 4

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

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