2. Use Stokes' Theorem to find the line integral of (2y, 3x, – 2) on C : the circle z? + y? = 4 in the ry-plane, counterclockwise when viewed from above. %3D

Q: Given The boundary of C: 0 ≤ x ≤ π,0 ≤ y ≤ sinx With Green's Theorem, Evaluate this line integral. $…

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Q: Evaluate the line integral fc (2 + x*y)s, where C is the half circle x + y? = 1 in the upper half…

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Q: Evaluate the integral for y'dx + z?dy + x²dz, where C is the triangular closed path joining the…

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Q: Evaluate the line integral ry dz for C : r(t) = (e , et+1)", te'), 0 <t<1 and then repeat with -C in…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Calculate the following line integral: Se y dx – x dy Over the four curves C given by the following…

A: To Determine :-  The line integral :  ∫C y dx - x dy over the given curves .

Q: Use Stokes' Theorem to find the line integral | (17 + 2y°)i + (w + =°)5 +(= + 2r*)k) • dř where C is…

A: Stokes' Theorem: Let S be a oriented smooth surface which is bounded by the curve C (simple closed,…

Q: Use Green's Theorem to evaluate the line integral below. | (2 - v?) dx + 5xy dy C: r = 1 + cos(0), o…

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Q: Use Green's Theorem to evaluate Se (y? – tan-1 (r)) dr + (3r + sin (y)) dy, where C is the boundary…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Evaluate the line integral, where C is the given curve. xevZ ds, C is the line segment from (0, 0,…

A: Consider the  line integral ∫Cxeyzds Where C is the line segment from (0,0,0) to (3,4,2).

Q: Evaluate the integral x² dx + y? dy where C consists of the arc of the circle x2 + y² = 4 from (2,0)…

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Q: (5) Use Stokes' Theorem to find the line integral |(* + 2y°)i + (y + z°) +(= + 2r*)k) • dř where C…

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Q: Use Green's theorem to evaluate the line integral frdx + (a - 20)dy where C is the boundary of the…

A:

Q: Can you show the steps on how to do this integral?

A: Consider the provided question, (3) Evaluate the integral by using the greens theorem,

Q: 3. Use Stokes' theorem to evaluate the line integral F· dr where A = -yi + xj and C is the boundary…

A: Stoke's theorem given by ∫CF.dr=∫∫Scurl A×n^ds According to the question, A=-y i+x j…

Q: Use Stokes' theorem to evaluate line integral| (z dx + x dy + y dz), where C is a triangle with…

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Q: Evaluate the line integral L(r – y*)dx + (1+ y² + =*)dy, where Cis the circle of radius 2 centered…

A: We have to evaluate the value of the integral

Q: Evaluate the line integral, where C is the given curve. (Round your answer to one decimal place.)…

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Q: Use STokes's Theorem to evaluate:- @ Line integral ) (K+Z)dx +Cx-y)dy+ x dz c is ellips de fined by…

A: We'll answer the first question. Since the exact one hasn't specified. Please re-submit the question…

Q: Use Green's Theorem to evaluate the line integral (T + 2y*) da + (e²y – 20*) dy - C where C is the…

A: Green's Theorem: Let R be a simply connected region with smooth boundary C, oriented positively and…

Q: Find an integral for the area of the surface generated by revolving the parametric curve about the…

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Q: Y – 5x |dA x + y 100 cos

A: We have to evaluate the double integral ∬ 100cosy-5xx+ydxdy over the region D where D is the…

Q: Evaluate the line integral, where C is the given curve. xy ds, C is the right half of the circle x2…

A: C is the right half of the circle x2+y2=16 thus the parameterization of the circle is x=4cos t and…

Q: Evaluate the line integral S, y ds where C:x = t²,y= 2t, 0 <t < 3

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Q: 3. Consider A(r) = (y, -x,0), and the line integral A• dr along the C boundary of the plane x + y +…

A: The given vector function is A(r)=(y,-x,0)., the line integral ∮CA·dr is along the boundary of the…

Q: Evaluate the line integral, where C is the given plane curve. | xy* ds, C is the right half of the…

A: Use parametric to solve

Q: Use Green's Theorem to determine the value of the following line integral 1 I - (7 x + 3 y ) dx + (…

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Q: Evaluate the surface integral SP ( – 2) // where S is the portion of the cylinder r2+22 = 1 above…

A: It is given that S is the portion of the cylinder x2+z2=1 above the xy plane between y=1 and y=2.

Q: 338. [T] Use a CAS and Stokes' theorem to approximate line integral /[(1 + ykdx + (1+ z)xdy + (1 +…

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Q: Evaluate the line integral, where C is the given curve. Sc zdx + xdy + ydz C: x = t, y = t³, z = tª,…

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Q: Evaluate the integral for Sy dx + z?dy + x²dz, where C is the triangular closed path joining the…

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Q: Evaluate the line integral, where C is the given curve. хуеу2 dy, C: х %3D 3t, у%3D 2t?, = 2t3, 0st<…

A: x=3t, y=2t2,z=2t3

Q: Use Green's theorem to evaluate the line integral along the given positively oriented curve. | (3y +…

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Q: Consider the line integral L(- In(2² + y°\j+ tan '(2)i). dr where C is the positively oriented…

A:

Q: Use Green's Theorem to evaluate the following line integral. Of dy -g dx, where (fg) = (7x2,8y?) and…

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Q: Evaluate the line integral, where C is the given curve. | xy? ds, C is the right half of the circle…

A:

Q: Use Green's Theorem to evaluate the following line integral. Of dy -g dx, where (f,9) = (7x?,8y) and…

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Q: Calculate the line integral a) |y ds, C:x =ť², y = 2t, 0 <t < 3 C

A: Use parametric to solve

Q: Use Green's theorem to evaluate the line integral I of the one-form W = + æ sin? (y)) dæ + (x²…

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Q: Evaluate the line integral ſc F·dr, where F = (y, 0, zy) and C is the helix given by (cost, sint,…

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Q: Use green's theorem to calculate the integral Fdr, F(x, y) = (e* + a²y , e" – xy² + sen(y) + 2)…

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Q: Evaluate the line integral, where C is the given plane curve. xy ds, C is the right half of the…

A:

Q: Use Stokes' theorem to evaluate line integral (z dx + x dy + y dz), where C is a triangle with…

A: Consider the provided question, We have to evaluate the given integral by using the stokes theorem,…

Q: Let M(x, y) = y - cos y and N(x, y) = x sin y. Use the Green's Theorem to calculate the line…

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Q: 3. (a) Use Green's theorem to evaluate the line integral 4 y* dx – a* dy where C is the positively…

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Q: Evaluate the line integral ∫C -y dx + z dy + 2x dz, where C is the helix r(t) = (cos t)i + (sin t)j…

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Q: Verify that both integrals in Stokes' Theorem are equal when F= (y – 2, z – 1, r – y), S is the cap…

A: Solve

Q: Evaluate the following line integral –2ª dx + (xª + 2x²y²)dy re where C is the boundary of the…

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Q: 2). Use Stokes' theorem to evaluate the integral 6 F • dř for F(x, y, z) = (x – y)î + (y – z)ĵ + (z…

A: Formula: By Stoke's theorem we have ∮C F · dr¯  =∫t=t1t=t2 F¯(r(t))r'(t) dt, where r(t) is…

Q: Use Stokes' Theorem to find the line integral (x+ 2y°)ï+ (y + z²)j+ (z + 2r²)k) · dř where C is the…

A: To find the line integral, Using stokes theorem.