Applying Stokes' theorem, solve the following integrals: (y² - xz) dx + (x² + zy) dy + (x2 + y) dz C curve intersection of the plane 2x + 2y + 2z = 1 with the paraboloidz = x? + y2

Q: -2z-22 Write the integral + y? dz dy dx in cylindrical coordinates. DO NOT EVALUATE THE INTEGRAL!!!

A: Triple integration problem....

Q: Applying Stokes' theorem, solve the following integrals: (y + x) dx + (x + 2) dy +z? dz C curve…

A: To evaluate the integral ∫Cy+xdx+x+zdy+z2dz, C curve of cone z2=x2+y2and the plane z=1.

Q: V2x-x² Write the integral 2 dz dy dx in cylindrical coordinates. DO NOT EVALUATE THE INTEGRAL!

A: We know that, the cylindrical coordinates in terms of the cartesian coordinates is given by,…

Q: 6. Evaluate the triple integral f, x?yz dV, B = {(x, y, z): - 2 < x<1,0 < y< 3,1<z<5}

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Q: Calculate the double integral || x + y)?e -r dx dy where R is the square with vertices (4, 0), (0,…

A: Given: ∫∫Rx+y2ex2-y2 dx dy where R is the square with vertices 4,0, 0,4, -4,0, 0,-4

Q: Convert the given integral into an integral in spherical coordinates. /16-х° 16- x (x² + y? + z?)²…

A: Convert the given integral.

Q: Green’s Theorem for line integrals Use either form of Green’sTheorem to evaluate the following line…

A: By Green's Theorem, we have where R is the region enclosed by curve C.

Q: 19. S elnx²dx 20. S y²e²y dy ,2y

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Q: valuate the line integral, where C is the given curve. z2 dx + x2 dy + y2 dz, C is the line segment…

A: Follow next step

Q: 1. Use integration in cylindrical coordinates in order to compute the vol- ume of: U = {(x, y, z) :…

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Q: 4. Change the Cartesian integral to an equivalent polar integral S'I SER dy dx e -(x²+y²) /2 re-r dr…

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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: (c) Use Green's Theorem to solve the line integral xy dx + x'dy where C is formed by the parabola y…

A: WE HAVE TO USE GREEN S THEOREM

Q: Verify Green's Theorem by evaluating both integrals aN | y? dx + x2 dy = dA ax ду for the given…

A: Gshhsg

Q: (b) Find the value of the following integrals: z-1 1- dz, y is the triangle with vertices at the…

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Q: Q2:-/ Use a variation of parameter method to find a particular integral of the equation x?y" - 2xy'…

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Q: he C +y* +z*)i dzdydz The product of the triple integration (using spherical coordinates)

A: Given

Q: Apply Green's Theorem to evaluate the integrals in Exercises 27–30. p (y? dx + x² dy) 27. C: The…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Calculate the line integral x y dx + x² y³ dy where C is the triangle with vertices (0,0), (1,0),…

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Q: Change the iterated integrals to spherical coordinates 1 VI-x VI-x-y? x²-y? 1 dzdydx x2 + y2 + z2 -1…

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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…

Q: ¹ // x² + y² + 2² dV, where E is the ball: x² + y² + z² ≤ 16. Use spherical coordinates to evaluate…

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Q: use Green 's Theorem to evaluate the line integral. Orient the curve counterclockwise unless…

A: Solution Given  ∮C y2 dx + x2 dy, where C is the boundary of the square that is given by 0 ≤ x ≤ 1,…

Q: 29-30 Evaluate the integral by changing to cylindrical coordinates. 29. , xz dz dx dy -y2 JVx²+y2…

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Q: Evaluate the line integral ∫AB(x+y)dx+xdy for two paths of integration: AB is the line segment from…

A: We need to find the following integral: a) AB is line segment from A(0,0) to B(1,1) b) AB is the…

Q: 16. Find the complete integrals of the foiowing equations: (i) z pq = p+4 che (i) p°q² +x?y? = x°q?…

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Q: SI. f dV here D is the solid region in the first octant between the elliptic cylinder 4x2 + 22 = 16…

A: Find the limits of x , y,z then compute integral

Q: 1- 2- 3- 3-Evaluate the integrals in Exercises: [ sect? (x - 1) dx sech² s sech Vt tanh Vt dt Vt…

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Q: Using Green's theorem in the plane, evaluate (x'y dy - x²y dx), where C is the triangle with…

A: As we know that; The Green's theorem: ∫CMdx+Ndy=∫∫R∂N∂x-∂M∂ydxdy Given: I=∫Cx3y2dy-x2y3dx So,…

Q: For what value. of4, the fundion Ux)= I+dx is. solution of %3D the integral equation x3= Ut dt

A: We have to first transform the x variable of u function to t.

Q: COS Z dz, 22 – 4

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Q: the value of the given integrals |z – i| = 2, (z € C) positive definite curve C around the circle…

A: The solution is given as

Q: 3) S. (3x? – 3yz + 2xz)dx + (3y? – 3xz + z²)dy + (3z2 - 3xy + x2 + 2yz)dz Calculate the curvilinear…

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Q: 4-y² c/4-x²-y2 |4-x²-y² 1 6. Given ſ S x²+y?+z? dz dx dy (b) Express the given integral as a triple…

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Q: 1/ Math

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Q: 17. Change the Cartesian integral to an equivalent polar integral (2 Points) e -(x²+y²) dy dx re -r…

A: Here we have a question in which given that double integral in Cartesian form. We have to find this…

Q: Use polar coordinates to evaluate the Gaussian integral -2x2 e dx. 8e-2a2

A: The objective here is to evaluate the given Gaussian integral using polar coordinate. Given Gaussian…

Q: The circulation line integral of F = (4xy´,2x° +y) where C is the boundary of {(x.y): 0 sys sinx, 0…

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Q: 3) Evaluate the cylindrical coordinate integrals in: (r*sin*e + z*) dz r dr de

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Q: az:/ Use a variation of parameter method to find a particular integral of the equation x?y" + xy'-y…

A: We can solve this using variation of parameters method

Q: Use cylindrical or spherical coordinates to evaluate the integral. 4-y² /8–x²-y² 19. z? dz dx dy 0.…

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Q: 2. The curve is given as a curve with positive direction in motion at the boundaries of the square…

A: Given,

Q: Use the indicated change of variables to evaluate the double integral. 16(x2 + y2) dA X = u + v) 4 y…

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Q: (v) y" – y = sech(x), y(0) = 0, y'(0) = 0. NOTE: sech(x) is the hyperbolic secant of x. In (v), it…

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Q: (1,0) (1,0) | (x2 – y²) dx – 2x y dy + i | 2x y dx + (x² – y²) dy (0,1) (0,1) Calculate the above…

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Q: (i) Evaluate the line integral T+y cos(ry)]dx+ [y + x cos(ry)]dy where U is the curve y = v from (1,…

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Q: 20. Given the path, x $ dx + xe dy determine the line integral using Green's theorem if C₁is y = x²…

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Q: V4 - x2 8- x2 – y 2 Convert the integral dz dy dx into an integral in spherical coordinates and…

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Q: Apply Green’s Theorem to evaluate the integrals ∮(3y dx + 2x dy)C: The boundary of 0≤ x ≤π, 0 ≤ y ≤…

A: According to Green's theorem - ∮Pdx+Qdy = ∬D dQdx-dPdydxdy          ...............(1)Given integral…