Use Green's theorem to evaluate the line integral |F•dš where F = 2xyi +(x – y²)j and C is the C path along the curve y = x' from (0,0) to (1,1) and x = y² from (1,1) to (0,0) .
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.
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Q: Evaluate the line integral, where C is the given curve. (x + 8y) dx + x2 dy, C consists of line…
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Q: Show that (2x In yz-5ye") dx-(5e* -x²y)dy +(x²z- +2=) dz, where C runs from (2,1,1) to (3,1,e), is…
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Q: Compute the line integral of F(x, y) = (x3, 4x} along the path from A to B in Figure 19. To save…
A: Given : F(x, y) = x3, 4x To compute the line integral of F(x, y).
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: Use Green's theorem to evaluate the line integral [F•dš where F = 2xyi +(x– y²)j and C is the path…
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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. yex dx…
A: Formulae used, d(ex)dx=ex d(x)dx=1and ∫abexdx=exab
Q: Evaluate the line integral, where C is the given curve. (x + 9y) dx + x² dy, C consists of line…
A: To evaluate the line integral, consider the curveC1 consisting of the line segment from0,0to9,1. The…
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 () in(x²+y?) oy 2 arctan Y dx + Inx2 C: x = 9 + 6…
A: Green's theorem is a vector identity which is equivalent to the curl theorem in the plane. Over a…
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Q: Evaulate the line integral of c (x^2+y^2) where c is the line segment from (-1,-1) to (2,2)
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Q: Evaluate the line integral along the given paths. C(x2 + y2) ds a) C: line segment from (0,…
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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: Use Green's Theorem to evaluate the line integral Jo (y - x)dx + (2x - y)dy for the given path. C: x…
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Q: line
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Q: Compute the line integral of f(x)=2x over the curve y=x² from (0,0) to (1,1). |
A: The line integral of f(x)=2x over the curve y=x2 from (0,0) to (1,1)
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: Consider the line integral xy dx + xy° dy with C the triangle with vertices (0, 0). (1,0), and (1,…
A: Given, the line integral Where C is the triangle with vertices.
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: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…
A: Line integral will be path independent if vector field whose integral we need is conservative…
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: Q2 Use Green's theorem to evaluate the line integral F•ds where F = 2xyi +(x-y')j and C is the path…
A: In vector calculus, Green's theorem relates a line integral around a simple closed curve C to a…
Q: Use Green's Theorem to evaluate the line integral below. dx + 5xy dy C: r = 1 + cos(0), 0 s0 s 2n
A: Consider the provided line integral ∫Cx2-y2dx+5xydy. Let M=x2-y2, and N=5xy. That implies,…
Q: Use the direct method to evaluate the path integral for the work done by F(x, y) = (y, -x) along…
A: -4π
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: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. S. cos…
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Q: 8.) Find work done by F = (2x³y* + x, 2x*y³ + y) along the path r(t) = (t cos(at) – 1, sin (t))…
A: Since we have given that F = 2 x3 y4 +x, 2 x4 y3 +y and rt=t cosπt-1, sinπ2t drt = cosπt -t…
Q: Justify the Fundamental Theorem of Line Integrals for F. dr in the case when F(x, y) = (8x + 8y)i +…
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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: Given that Take, Now, so, Then then by comparing
Q: Show that the line integral is independent of path and evaluate the integral. integral C…
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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: Evaluate the line integral | F•ds where F = 2xyi +(x – y²)j and C is (a) y=x from (0,0) to (1,1) (b)…
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Q: Compute the path integral of F = ⟨ y , x ⟩ along the line segment starting at ( 1 , 0 ) and…
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Q: Use Green's Theorem to evaluate the line integral of F (x°, 9x)
A: Given, the line integral of F=x3, 9x around the boundary of the parallelogram in the following…
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: Use Green's Theorem to evaluate the line integral below. √ (x² − y²) dx + 7xy dy C:r = 1 + cos(8), 0…
A: Given integral is ∫Cx2-y2dx+7xy dy where C: r=1+cosθ, 0≤θ≤2π To Use: Green's Theorem to evaluate…
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: 7. Verify Green's Theorem for O (6+ x²) dx + (1 – 2xy) dy where C' is shown below by (a) computing…
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Q: Evaluate the following line integral I=[3x°dx + 2yzdy +y°dz from A: (0, 0, 0) to B: (2, 4, 8) a) By…
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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: Compute the integral ∮C [(cos x − 3y) dx + (2x − sin y) dy], where C is the closed curve that…
A: The region of integration C is divided into three line segments C1, C2 and C3. Let C1:y=0,…
Q: Evaluate line integral F. dr, where F(x, y) =(2xy)i + (x²+3)j, and C is the path given by r(t) = t =…
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- Let F=2(x + y)7+4 sin(y). Find the line integral of around the perimeter of the rectangle with corners (3,0), (3, 6). (-3, 6), (-3,0), traversed in that order. line integralEvaluate the line integral (8x + 7y)dx + (2x - 7y)dy along the | curve C: r = 8 cos t, y = 16 sin t (0 < ts-) T NOTE: Enter the exact answer. | (8x + 7y)dx + (2x – 7y)dy =Calculate the line integral f (−xy³ − 6x + 6y − 3) dx + (−5xy − 3) dy, - where C' is the rectangle with vertices (-2, 1), (2, 3), (-4, 3), and (-4,1) oriented clockwise. Enter an exact answer. Provide your answer below: f(-x³-6x+6y-3) dx + (−5xy − 3)dy =
- Let F = 5(x + y) 7 + 7 sin(y) j. Find the line integral of Faround the perimeter of the rectangle with corners (2,0). (2,6). (-3, 6). (-3,0), traversed in that order. line integral|Use a linear approximation to estimate the change in f(x, y, z) = e2* cos(5yz) when moving from the origin a distance of 0.5 units in the direction of (5, 4, 1). Change in f is approximatelyCalculate the line integral (F•dr, where F 3x yi + x'j in two cases for Ci and C2. These two curves start and end at the same points. a. Ci is the curve y = 2x² with x ranging from -1 to +1. Draw a graph showing the curve Ci and then calculate (F•dr. b. Cz is the straight line that goes from x = -1, y = 2 to x = 1, y = 2. Draw a graph showing the curve C2 and then calculate [F•dr. As a check in this question you should get the same answer for both integrals because the vector field F = 3x° yi + x'j is the gradient of an associated scalar function , f (x, y) = x³y and C1 and C2 start and end at the same points.
- Let F = 2(x + y)i + sin(y) 7. Find the line integral of Faround the perimeter of the rectangle with corners (4,0), (4,8), (-2, 8), (-2, 0), traversed in that order. line integral =a) Find the derivative of f(x, y, z) = 4zx3 - xy2 - z, at P.(1,0,2) | in the direction of v = 4i – 5j + v40 k.Use differentials to estimate the change in f (x, y, z) = x² ln(5yz + 1) as (x, y, z) changes from (2, 1, 3) to (1.99, 1.02, 3.05).
- Let F = 14xe¹ i +7x²e j and G = 14(x - y)i +7(x + y) 3. Let C be the path consisting of lines from (0, 0) to (7,0) to (7, 2) to (0, 0). Find each of the following integrals exactly: (a) [c F . dĩ = (b) ScĞ·dr =Does f(z)=z/(sin z)^2 have a pole of order 1 or 2 at z=0?Find div F and curl F if F(x, y, z) = 4y®z°i – 11x³2³j – 5xy'k. ,65; div F= curl F=