Q2) Evaluate each side of Stokes theorem for a portion of cylinder : p=2m 0<¢

Q: 2 ² J z=0x= -√4-2² 4-x²-2 y=0 N dydxdz

A: The given integral is: ∫z=02∫x=-4-z24-z2∫y=04-x2-z2 z dy dx dz Convert the given integral into…

Q: Consider the flow due to the sudden acceleration of a flat plate (Stokes' first problem) from…

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Q: Let F = %3| Use Stokes' Theorem to evaluate curlF · dS , where S is the hemisphere x? + y? + z² =…

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Q: Compute the Jacobian for the change of variables into spherical coordinates: x = p sin o cos 0, y =…

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Q: Use spherical coordinates. Evaluate ∭z dV, where E is between the spheres x ^ 2 + y ^ 2 + z ^ 2 = 16…

A: Triple integral is used to integrate function of three variable in three dimensional region.

Q: Q2) Evaluate each side of Stokes theorem for a portion of sphere :r=2m, O=t/3, 0<¢<a H= 2r cosO sino…

A: This question is about application of Stokes theorem

Q: I = y dx + (z — х) dy — ydz, Jc

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Q: 2. Use spherical coordinates to evaluate the triple integral ||| æe xe²²+v²+z dV , where E is the…

A: Given:

Q: Q2) Evaluate each side of Stokes theorem for a portion of sphere :r=2m, e= T/3, 0<¢<a H= 2r cosO…

A: This question is about application of stkoes theorem

Q: When converting the triple integral to spherical coordinates, it becomes of the form V9-x² -y² vターx。…

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Q: erify Stokes Theorem for the ve lane x + y + z = 1 bounded b orientation.

A: It is given that F→=3x,2x-y,3y is a vector field on plane x+y+z=1 bounded by x=0, y=0 and z=0 with…

Q: 3.) Verify the conclusion of Stokes' Theorem given F(x,y,z)=(x-y,y-z,z–x) where S is the surface cut…

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Q: Evaluate the cylindrical coordinate integral. 1/2 18 1/r cos 0 dz r dr d0 0 9 1/?

A: Given that triple integration problem or cylendrical coordinate problem .we use simple integration…

Q: Determine the area of the surface with parametric equat ions x = 2u?, y = v², z = 2uv, %D 0<u< 3, 0<…

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Q: Q2) Evaluate each side of Stokes theorem for a portion of cylinder : p=2m 0<¢ <a /3, 1<z<2 H= I z…

A: according to stokes therem, line integral(H.dl)= surface integral(curl(H).ds) for evaluating line…

Q: 2. Change the following integral to spherical coordinates * ... JI 1-x²-y² dzdydx p sin ø cos o dp…

A: We will find out the required expression.

Q: Question 2: Use Stokes' Theorem to evaluate F dr where F = y²i+z²j+x²k while C is the boundary of…

A: Integral represents the line integral of a vector field over the closed line. This type of integral…

Q: / Use Stokes theorem to evea luarte the SS Canl F.n ds, S being that Part of the Sar face of the…

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Q: 6) Use Stokes' Theorem to compute ,(V × F) · ndS where S is the portion of the tetrahedron bounded…

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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: Let F = 0, oriented upwards

A: Stokes theorem

Q: Let S be the boundary of a cube with side length 1 in octant 1. Use Stokes Theorem to evaluate Se…

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Q: Use Stokes' theorem to evaluate      CF · dr  where C is oriented counterclockwise as viewed from…

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

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Q: A fluid motion is given by V=(y+z)i+(z+x)j+(x+y)k. Is this motion irrotational? If the velocity…

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Q: Compute the shared mass between the polar curves (r 2a cose) and (T = 2a sine) use density equal to…

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Q: Change the iterated integrals to spherical coordinates 1 v1-r? /1-x²-y? dzdydx a2+y2+z2 -1 V1-x² -y?…

A: The relation between the cartesian and spherical co-ordinates is given by: x=ρ sinϕ cosθy=ρ sinϕ…

Q: Convert 18-22-y2 22 +y? +z dz dz dy into spherical coordinates. Hence evaluate the integral.

A: The volume of a solid can be calculated using the triple integrals in the spherical coordinates. The…

Q: Verify Stokes' Theorem for F(x, y, z) = xi + yj + y²zk where S is the first octant portion of the…

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Q: The planet is spherical with a radius of 1 unit in length. Suppose that in a coordinate system whose…

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Q: - Prove Stokes' Theorem by verifying it for F= [y,z,x] and S the paraboloid. %3D te CEY2=(x, y) = 1…

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Q: 8. Set S be the bondary of the cube with side length 1 in Oc tant 1. Is in 6 pieces) Use Stokes…

A: (1) Over the surface ABCD ∫sx dy dz +z dz dx=∫01dz∫01xdy…

Q: Let F = . curlF dS, where Use Stokes' Theorem to evaluate S S is the hemisphere a + y? + z² = 16, z…

A: Given that F=x2eyz,xexz,z2exy Then S is the hemisphere x2+y2+z2=16 The objective is to find the…

Q: 3. Suppose F z = 4 – a? – y? above the r- y plane, oriented upward. Calculate fe F dĩ in two ways:…

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Q: Let S be a square plate with boundary C having length of each side as 2 units, lying in the plane z…

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Q: Evaluate the integral 1 V1-y² V2-x²– y² (x² + y? + 2?) dzdxdy 2+y² by changing it to spherical…

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Q: The motion of a fluid particle is defined parametrically as follows, r(t) = sinh(t), and y(t) =…

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Q: Evaluate Triple Integral H (6 − x2 − y2) dV,  where H is the solid hemisphere  x2 + y2 + z2 ≤ 16,…

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Q: 7. Use spherical coordinates to find ||| z dx dy dz where E is the solid defined by E Os Vr* +y³ <z…

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Q: 2. Use Stokes' Theorem to evaluate curlF.dS whereF = 2y i + 3z j+(z – z) k and S is the portion of y…

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Q: Use cylindrical coordinates. Evaluate the triple intergral   5(x3 + xy2) dV, where E is the solid…

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Q: (10) Sketch the solid bounded by z = x2 + y? and z 4- x2 - y². Use cylindrical coordinates to find…

A: Given ∫∫∫Dx2+y2dVand solid bounded by z=x2+y2 and z=4-x2-y2

Q: A fluid has density 600 kg/m3 and flows with velocity ū = ri + y. measured in meters, and the…

A: Here we have, Velocity v→=xi^+yj^+zk^ where x,y, and z are measured in meters.  the equation of…

Q: State the Stokes' Theorem. Ise the Stokes' Theorem as stated in (a) to evaluate the lin |F- dř here:…

A: We have to write the stokes theorem and using it We have to find the given line integral according…

Q: Let F = ( ) 5x* + 16z, 2x³ + 3y² + 16z, x + y + eVz³+1 and C be the curve defined by 7(t) = (2…

A: Given that,  F=5x4+16z, 2x3+3y2+16z, x+y+ez3+1 And rt=2cost, 2sint, 16cos2t sin2t, o≤t≤π To find…

Q: 4. Convert the integral to spherical coordinates and evaluate the integral. V49 - x S. 49 - x2 2 –…

A: Solution: To find-          ∫07 ∫049-x2 ∫049-x2-y2  x2+y2+z2  dz dy dx

Q: Without using the formula (Stokes), calculate l=∂S∫F(x).T(x)dl, where F(x) =x1x2i + x2x3j + x1x3k, e…

A: Consider the given : F→=x1x2i^+x2x3j^+x3x1k^ over the surface of northern hemisphere x12+x22+x32=16…

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: Sfcurt Use Stokes' theorem to evaluate rl F•dS where F= and S is the hemisphere x2+y²+z²=9, z 20,…

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Q: Convert to cylindrical coordinates and evaluate the integral 5 /25–x² 6 !!! dzdydx x² + y- 0 0 0

A: Conversion of cartesian co-ordinates into cylindrical co-ordinates. φ is angle made by vector with…