Evaluate the line integral x +1 ds /1+4x² Vĩ where C is the part of the parabola y = 9 – x² from (-3,0) to (0,9).

Q: Evaluate the line integral / Vxy° +3 dx +6xy" dy, where C any curve joining (1, -1) to (16, 1).

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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 the line integral along the path C given by x = 2t, y = 4t, where 0 <ts 1. (y - x) dx +…

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Q: 8.Evaluate the triple Integral. Te by The paraboloid X=2yt + 2z? and the plane X=2. 7x dV, where E…

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Q: Evaluate the line integral -ydr + rdy along the curve C : y² = 6x from (6, 6) to (0,0). NOTE: Enter…

A: The given line integral is ∫c-ydx+xdy along the curve c: y2=6x from (6,6) to (0,0)

Q: Evaluate the line integral f e-*(cos y dx - sin y dy), where c is the rectangle with vertices (0,0),…

A: The line integral function is ∫Ce-xcosydx-sinydy. The vertices of the rectangle is 0, 0, π, 0, π,…

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: Use Green's Theorem to evaluate the line integral |v - x)dx + (2x – y)dy for the given path. C: x =…

A: Answer

Q: Evaluate the line integral y = x² from (-1, 1) to (1, 1) and the line segment from (1, 1) to (−1,…

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Q: Evaluate the line integral. y dx - x dy, parabola y = x² for 0 < x < 8

A: Given:

Q: Evaluate the line integral C: y² = 27x from (27, 27) to (0,0). NOTE: Enter the exact answer. 6-₂…

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Q: Evaluate the line integral (x+2y)dx + dy, where C consists of the path C from (0,0) to (3,0), the…

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Q: evaluate both the line integral and the double integral. 16. P(x, y) = 2x – x³y°, Q(x, y) = x³y°, C…

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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: 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 along the path C given by x = 2t, y = 4t, where 0 ≤ t ≤ 1. √(²x- (y - x)…

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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: Evaluate the line integral/ (ax + 2y)dx +x dy, where C consists of the path C from (0,0) to (3,0),…

A: Consider the provided question, Hello. Since your question has multiple sub-parts, we will solve…

Q: State two other forms for the line integral ∫C F ⋅ n ds given that F = ⟨ƒ, g, h⟩ .

A:

Q: Evaluate the line integral xyld x + (x²+y)dy] +. where c is the saruare farmed by the lines

A: Let us consider a line integral ∫CP dx+Qdy then it can be written as  ∫D∫∂Q∂x-∂P∂y dA  Where, P and…

Q: Evaluate the line integral | 27x²yzds with respect to s along the curve C : x = t, y = t³, z = ; t(0…

A: The line integral is ∫C27 x2 y z ds x=t, y=t3, z=23t30≤t≤1  dxdt=1, dydt=3t2, dzdt=2t2

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

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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 [39a²³yzds with respect to s along the 2 curve C: x = t, y t, y = t²,₁…

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Q: (a) Verify that the Fundamental Theorem for Line Integrals can be used to evaluate the integral Sc…

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Q: *0 = x = 0, y = 1, x = y about the line y = 1 can be computed using the method of disks or washers…

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Q: Evaluate the line integral ,F. dr where F = (sin x, –2 cos y, 5xz) and C is the path given %3D by…

A: Integral F.dr = integral F(r(t)).r'(t) dt

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

A:

Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 ≤ t ≤ 1. [(x + 3x²) dy

A: To evaluate: ∫C(x+3y2)dy...(1) where C is given by x=2t, y=4t⇒dy=4dt and 0≤t≤1

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).

A:

Q: Describe the bifurcation for the following dy - Ay - y %3D dt

A: The saddle node-bifurcation: Let y˙=f(α,t) is the system of equation, the to find the saddle-node…

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 along the path C given by x = 2t, y = 4t, where 0<ts 1. (y – x) dx +…

A: Just I have used the given parametric representation of the curve C to change the given line…

Q: Use Green's Theorem to evaluate the line integral (y – x)dx + (2x – y)dy for the given path. C: x =…

A: Given integral is ∫Cy−xdx+2x−ydy where C:x=2cosθ,y=sinθ,0≤θ≤2π. Green theorem is given by…

Q: Evaluate the line integral Jo 9x²yzds with respect to s along the с 2 curve C: x=t, y = t², z = /t³…

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Q: Use the Green's Theorem to evaluate the line integral 2xydx + x² – y² dy where C is the curve…

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Q: Use Green's Theorem to evaluate the line integral. y dx + 7x dy C: square with vertices (0, 0), (0,…

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

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Q: Evaluate the line integral ∫Cxdy−ydx along the curve C defined by the equation y=x3 from the origin…

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Q: 6. Use Green's Theorem to evaluate the line integral fc 2xy dx + (x² + y²) dy, if C is the ellipse…

A: Let R be simply connected region with a piecewise  smooth boundary  'C'. If functions 'M' and 'N'…

Q: Evaluate the line integral |(2? + y) dx – x dy where C is the line segment from (2,5) to (5,9) in…

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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: 11 Calculate the line integral f Gy)ds for the given junc rion and path xiyl=xy KHt)=<3+,2t=-37 for

A: r(t)=&lt;3t,2t-3&gt;=&lt;0,-3&gt;+t&lt;3,2&gt; x(t)=3t  and y(t)=2t-3 ds=32+22dt=13dt 0≤t≤1

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: 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: Use the Fundamental Theorem of Line Integrals to find the exact value of the path-independent line…

A: First of all hare we check for the path independent line integral then solve for moving over the…

Q: Evaluate the line integral 9x²yzds with respect to s along the 2 curve C: x=t, y = t², z = t³(0 ≤ t…

A: Given: ∫C9x2yzds x=t y=t2 z=23t3 0≤t≤1 To find: Value of the given integral.

Q: (2x + y)dx + (x + 2y)dy

A: Given integral is:  where C is any curve that joins the point (1,1) with the (2,2).

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.