(yx + 3xsiny + 3y) dx + (x° cosy – y° + 3x) dy along the curve C that is a square oriented counterclockwise with vertices (0,0), (1,0), (1,1) and (0, 1). Consider the line integral

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: a) Evaluate Vx² + y² dydx. 1 J-Vi b) Evaluate the line integral | cos x cos y da + (1 – sin æ sin y)…

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Q: sin y dV, where E lies below the plane z = x and above the triangular region with vertices (0, 0,…

A: Given, the region E lies below the plane z = x and above the triangular region with vertices 0,0,0,…

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: 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: Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise. 2x + 3y dx + e…

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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: 6. Evaluate the line integral (x? + y² )dx – x dy along the curve C: x? + y² =' counterclockwise…

A: Given: ∫c x2+y2 dx- x dy  We have to Evaluate the given line integral along the curve C: x2+y2=1…

Q: Evaluate f(x + 2y)dx + (y – 2x)dy around the ellipse C defined by x = 4 cos 0, y = 3 sin 0,0 < 0 <…

A: Given the Integral : ∮c(x+2y)dx-(y-2x)dy ⇒Let I=∫C(x+2y,y-2x).(dx,dy) , x=4cosθ and y=3sinθ…

Q: Find the differential of w = x ev sin z at the point (x, y, z) = (1, 1, 0). %3D O dy + dz O dy O dx…

A: Obtain the differential of the given function as follows. w=xeysin zdw=ddxxeysin zdx+ddyxeysin…

Q: Suppose F(x, y) = -y sin(x)i + cos(x)j. (a) Find a vector parametric equation for the parabola y =…

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Q: Assuming that C is the counterclockwise oriented boundary curve of the unit square in the first…

A: It is an simple and easy question on vector calculus  Can be easily solve by use of green's theorem

Q: 2. Use Green's theorem in order to compute the line integral P (x – 4)³ dy – y³ dx where is the…

A: We need to compute the given integral using Green's theorem . ∮C(x-4)3dy-y3dx Where is the circle of…

Q: Use Green's Theorem to calculate line integral o sin(x²) dx + (3x – y) dy where C is a right…

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Q: dz (a) Use an appropriate form of the chain rule to find dx dz in terms of y in terms of x and if z…

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Q: (a) Find a function f(x, y, z) which satisfies Vf = (y + 2z, x + 3z, 2x + 3y). (b) If C is the curve…

A: Let the function f(x, y, z) = xy + 2xz + 3yz which satisfies the given property  Gradient (f) = ( y…

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: Calculate the double integral (x + y)²ex* - y² dx dy where R is the square with vertices (2, 0), (0,…

A: According to the given information, it is required to find the integral over R where R is square.

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

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Q: Suppose F(x, y) = -y sin(x)i + cos(x)j. x? from the origin to the (a) Find a vector parametric…

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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: Evaluate the line integral (e*y+ 2x) dx + (e* + 1) dy, where C is a smooth curve from the point (0,…

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Q: Evaluate the line integral f (-y sin(xy)i – x sin(xy)j) dr using the potential function f(x, y) =…

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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: Given the scalar function f(x,y)=2xy,calculate the line integral along the ellipse curve from point…

A: Given data:- The given curve is, x29+y24=1 The given scaler function is, f(x,y)=2xy t E 0,π/2

Q: Use Green's theorem in order to compute the line integral (2sin z + 3y²) dx + (sin(4®) + 2x³) dy…

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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 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: Evaluate the unoriented line integral (2æ² + y² + z²) ds along the parametric curve a : [0, 1] → R³…

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Q: Suppose F(x, y) = -y sin(x)i + cos(x)j. Find a vector parametric equation for the parabola y = x²…

A: The solution is following.

Q: 5) Evaluate the line integral S YX²dX + XY²dY on curve C, where C is the upper portion of the www m…

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

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Q: | 5y? dx +xy dy

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Q: (a) Find a function f(x, y, z) which satisfies Vf = (y + 2z, æ + 3z, 2x + 3y) (b) If C' is the curve…

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Q: Given the scalar functionf (x, y) = 2xy, calculate the line integral along the ellipse curve ²² +²²=…

A: We have to find the line integral along the given curve.

Q: Find the work done in moving a point charge Q- - 20 1C from.the origin to (4,0,0) m in the ficld E-+…

A: To find - Find the work done in moving a point charge Q = -20 μC from the origin to 4, 0, 0m in the…

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 line integral F. dr where F = (-3 sin x, cos y, 5xz) and C is the path given by r(t) =…

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Q: (c) Evaluate the line integral 2.xycdx + (x-y)dy where C is from (1,3) to (0,0) along the parabola…

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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: 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 unoriented line integral +y² + z²) ds along the parametric curve a : [0, 1] → R³ with…

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Q: Suppose F(2, y) = -y sin(æ)i + cos(2)j. (a) Find a vector parametric equation for the parabola y =…

A: Given F→(x,y) = -ysin(x)i→+cos(x)j→ a) Let us assume x=t then y=x2=t2 by differentiating r→(t) with…

Q: Evaluate the line integral: f y² dx + x² dy by parameterizing C where the curve C is a square R with…

A: According to the given information, it is required to evaluate the line integral.

Q: dy _ у-х dx 1+x y(0) =1 at the point x=0.1

A: Given differential equation is dydx=y-x1+x,y0=1.

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).

Q: Find the coordinates of the centroid of the curve x = cos t + t sin t, y = sin t - t cos t, 0…

A: Given,

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: 1. Evaluate the line integral I = = [v¢4x° + y*) dx + x(2x° + 3y*) dy] around the ellipse x/a? +…

A: The given line integral is, I=∮y4x2+y2dx+x2x2+3y2dy We know the Green's theorem:…