Using Green’s theorem, compute the line integral of the vector field below, along the curve x^2...

Using Green’s theorem, compute the line integral of the vector field below, along the curve x^2 - 2x + y^2 = 0 , with the counterclockwise orientation. Don’t compute the FINAL TRIG integral.

F(x,y) = < (-y^3 / 3) - cos(x^7) , cos(y^9 + y^5) + (x^3 / 3) > .

Expert Solution

milcah answered 2 years ago

Using Green’s theorem, compute the line integral of the vector field below, along the curve x^2-2x+...

Using Green’s theorem, compute the line integral of the vector field below, along the curve x^2-2x+ y^2=0 , with the counterclockwise orientation. Don’t compute the FINAL TRIG integral. F(x,y)=<- y^3/3-cos⁡(x^7 ) ,cos(y^9+y^5 )+ x^3/3> .

Compute the line integral of the vector field F(x, y, z) = ⟨−y, x, z⟩ along...

Compute the line integral of the vector field F(x, y, z) = ⟨−y, x, z⟩ along the curve which is given by the intersection of the cylinder x 2 + y 2 = 4 and the plane x + y + z = 2 starting from the point (2, 0, 0) and ending at the point (0, 2, 0) with the counterclockwise orientation.

In order to apply Green’s theorem, the line integral of the boundary should be evaluated such...

In order to apply Green’s theorem, the line integral of the boundary should be evaluated such that the integration region inside the boundary lies always on the left as one advances in the direction of integration. What happens if the region lies on the right? How can you apply the theorem then? Explain.

Vector Analysis: Verify Green’s Theorem in the plane for ? ⃑ = (?^2 + ?^2)?̂+ (?^2...

Vector Analysis: Verify Green’s Theorem in the plane for ? ⃑ = (?^2 + ?^2)?̂+ (?^2 − ?^2)?̂ in the anti-clockwise direction around the ellipse 4?^2 + ?^2 = 16.

Use the extended divergence theorem to compute the total flux of the vector field F(x, y,...

Use the extended divergence theorem to compute the total flux of the vector field F(x, y, z) = −3x2 + 3xz − y, 2y3 − 6y, 9x2 + 4z2 − 3x outward from the region F that lies inside the sphere x2 + y2 + z2 = 25 and outside the solid cylinder x2 + y2 = 4 with top at z = 1 and bottom at z = −1.

Compute the derivative of the given vector field F. Evaluate the line integral of F(x,y,z) = (y+z+yz , x+z+xz , x+y+xy )

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The flow of a vector field is F=(x-y)i+(x^2-y)j along the straight line C from the origin...

The flow of a vector field is F=(x-y)i+(x^2-y)j along the straight line C from the origin to the point (3/5, -4/5) A. Express the flow described above as a single variable integral. B. Then compute the flow using the expression found in part A. Please show all work.

Verify the Divergence Theorem for the vector field F(x, y, z) = < y, x ,...

Verify the Divergence Theorem for the vector field F(x, y, z) = < y, x , z^2 > on the region E bounded by the planes y + z = 2, z = 0 and the cylinder x^2 + y^2 = 1. By Surface Integral: By Triple Integral:

Problem 1: Use Green's Theorem to evaluate the vector line integral ∫C [?3??−?3] ?? where ?...

Problem 1: Use Green's Theorem to evaluate the vector line integral ∫C [?3??−?3] ?? where ? is the circle ?2+?2=1 with counterclockwise orientation. Problem 2: Which of the following equations represents a plane which is parallel to the plane 36?−18?+12?=30 and which passes through the point (3,6,1) ? a). 6?−3?+2?=3 b). 6?+3?−2?=34 c). 36?+18?−12?=204 d). 6?−3?+2?=2 e). 36?+18?+12?=228

(8pts)Consider the following vector field F and closed oriented curve C in the plane a. compute...

(8pts)Consider the following vector field F and closed oriented curve C in the plane a. compute the circulation and interpret the result b. compute the flux of the vector field F across C F = <y,-2x>/sqrt(4x^2+y^2) r(t) = <2cost,4sint>

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