Evaluate the line integral x²z ds, where C is the line segment from (0,6, 2) to (8, 5, 1).

Q: Find the line integral of x ds over C where c is the line segment from (1,0) to (0,1) using two…

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Q: Find the line integral of f (x, y,z) = -x + y + z over the straight-line segment from (1, 2, 3) to…

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Q: Evaluate the line integral, where C is the given cu curve. (x + yz) dx + 2x dy + xyz dz, C consists…

A: C consist line from A (2, 0, 1) to B(3, 3, 1) Now,

Q: Find the line integral ye-xz ds Here, C is the path r(t) = [t,3t,-6t], 0sts In(8) ·

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Q: Verify the Green's Theorem to evaluate the line integral . (2y²dx + 3xdy),

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Q: Evaluate the line integral x'z ds, where C is the line segment from (0, 5, 2) to (4, 6, 5).

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Q: Evaluate the line integral xyz ds where C is the line segment joining the points (1, – 1, 1) to (1,…

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Q: Compute line integral of F(x,y) = (2x² – 3,₁²³)^² + (2x +34²) ↑ с over the following C F-dr SCF ¾ ç…

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Q: Evaluate the line integral Lav where C is given by the line y = lnx, 1 ≤ x ≤e. xy ds,

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Q: Evaluate the line integral x +1 ds /1+4x² Vĩ where C is the part of the parabola y = 9 – x² from…

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Q: Evaluate the line integral [x(1 с where C is given by the line r(t) = (1 + 3t, 2t), 0≤ t ≤ 1. x(1 +…

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Q: Compute the line integral -xdy + ydx 2(x-y)2 +4xy where L is the circle (1-x)2 + y2 = 3 with a…

A: We can write the given line integral as ∫L y2x-y2+4xydx+-x2x-y2+4xydy, where L is the circle…

Q: Evaluate the line integral of x^3(z)ds, where C is the line segment from (0,8,2) to (7,4,6).

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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 line integral / x°z ds, where C is the line segment from (0, 2,4) to

A: Line integral: - The function to be integrated is determined along a curve in the coordinate system…

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

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Q: a) Evaluate the line integral TM UTM in terms of 7 where F = cos yi+ rj + ye*k and C is the line F…

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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: 2. Evaluate directly the line integral fo a dy where C is the quarter-circle from (0, 4) to (4, 0)…

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Q: . Compute the line integral of E from B(0,0,0) to A(2,1,3) if E = -4xya, – (4y + 2x2)a, + 8zaz. Use…

A: The line integral of vector field E→ along curve C is ∫C   E→.dr=∫abE→(r→(t).r→'(t)dt  where r(t)→…

Q: Evaluate the given line integral. I (y, –x) · dR, where C consists of 4y = x² from (-2, 1) to %3D C…

A: Line integration of the function

Q: Evaluate the line integral fe y dx + x dy where C is the parameterized path x = , y = f, 3 <iS9.…

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Q: Evaluate the line integral [F-ds where F = 2xyi +(x-y³)j and C is (a) y =x from (0,0) to [10] (1,1)…

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Q: Evaluate the line integral ∫Cydx+xdy along the curve y=x2 from the point O(0,0) to the point A(1,1)…

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Q: Evaluate the line integral Say dx +z dy, where C is the line segment from (-1, 1, 2) to (2, 3, 1).

A: Evaluate the line integral ydx +zdy where C is the line segment from (-1,1,2) to (2,3,1). Here i…

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 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: If C is the line segment from (1,3) to, (0, 0), find the value of the line integral: S(3y² i +3x}) ·…

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Q: 2. Evaluate the given line integral, (x – y, y) · dR, where C is the line segment from (0, 1) to…

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Q: Find the line integral of f(x,y,z) = -x+y+z over the straight-line segment from (1, 2, 3) to (0, −1,…

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Q: Evaluate the triple integral. 10x dV, where E is bounded by the paraboloid x = 5y? + 5z2 and the…

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

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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: Compute the line integral of f(x)=2x over the curve y=x^2 from (0,0) to (1,1)

A: Given query is to find the the line integral for the y = 2x over y = x2.

Q: 2. Compute the line integral of f(r, y) = r over the curve C, where C is a triangle formed by…

A: Now we have to find the line integral: ∫C x dswhere C is triangle joining the points:  (0, 0),  (1,…

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: Find the line integral of f(x,y,z) = -x + y+z over the straight-line segment from (1, 2, 3) to (0,…

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Q: Evaluate the line integral y² dx + x²y dy where C' is the rectangle with vertices (0,0), (5,0), (5,…

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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 triple integral. 4x dV, where E is bounded by the paraboloid x = 7y2 + 7z² and the…

A: Thanks for the question :)And your upvote will be really appreciable ;)

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: Compute the line integral of F = (-y, x) along the line segment from (0,0) to (1,1).

A: The line integral is evaluated using the following formula  ∫cF→x,yds=∫abF→rtr'tdt    , a≤t≤b   ,…

Q: O Evaluate the line integral over The Cur ve C. SCx+y+2)dx +6x +y-2)dy+ (x-y+2)dz where c is the…

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Q: Evaluate the triple integral. 8x dV, where E is bounded by the paraboloid x = 7y2 + 7z2 and the…

A: here, E is bounded by the paraboloid  x=7y2+7z2  and the plane x=7.    so , at    x=7 ,     y2+ z2…

Q: Evaluate the given line integral. | (y, -x) dR, where C consists of 4y = x² from (-2, 1) to (2, 1)…

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Q: Evaluate the line integral y dx + x dy where C is the parameterized path x = = ² , y = t° , 3 -ydx +…

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Q: dl /x² + y² + 4

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Q: Use Green's Theorem to Calculate the Line Integral ſy²dx + x²dy, where c is the triangle o vertices…

A: Given that, the line integral is ∫y2dx+x2dy and the vertices of the triangle is 0,0,4,0 and 4,4. By…

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.