What is the relationship between Green’s Theorem and Stokes’ Theorem?

Q: E dx (V × E) ·d Á

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Q: A disk rotates about an axis through its center. Point A is located on its rim and point B is…

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Q: X p(x, y, z)=xz²+sin (y) ex

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Q: sech Vt tanh V dt Vi

A: Given : Intergral sech √t tanh √t dt / √t

Q: A particle of mass m is moving under the force of attraction of another particle of mass m1 at a…

A: When a force F is applied to an object of mass m, the position of body changes. According to…

Q: 3 Z Eii %3D From the properties of characteristic equation of strain Zɛ, -Mw -Mw

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Q: Find tan * using lutegration by parts

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Q: nasin(hx) cos(bx)dx

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Q: Consider the shaded area shown in (Figure 1) Suppose that a 100 mm, b= 150 mm and r=80 mm Part A…

A: Given that a=100 mm, b=150 mm and r=80 mm. So, the moment of inertia formula is, Iy=∫aby(f(x)-g(x)dx…

Q: Find the work done by the force field

A: F→=x i→-y j→C:x(t)=t  ,  y(y)=t3/2r⇀(t)=<t,t3/2>dr⇀=<1,32t1/2>dtF(r(t))=t i→-t3/2 j→Work…

Q: Find the moment of inertia: y = x - x²; y = 0 about y = 0.

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Q: ula 0ニ こ0 2

A: Find solution using variable separation.

Q: Find the equation of the tangent line to the parametric curve at (1, 3). z =1+ Int y = t +2

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Q: Q4 (a) Define Gauss's theorem and Stokes' theorem.

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Q: Use Stokes' theorem to calculate c

A: Given,        F=xzi^+2zj^-xyk^ and C is the intersection of the plane y=z+2 with cylinder…

Q: find the equation of the plane tangent line anch normal r= Cost cos (et) Cost Simlz) } + Sint Ŕ

A: Given that, r=costcos2ti→+costsin2tj→+sintk→

Q: Solue D.E dy + (y cotx Sina) de = o

A: Solving

Q: soluti ly +y Ix

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Q: cos(48°) Use differential to approximate the value of

A: Cos 48° The nearest value to 48 whose cosine value can be taken is 45.Let us consider :x = 45° and…

Q: Find the tangential and normal components of acceleration for the positio denoted by ř = (cos 2t,–…

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Q: Can Stokes' Theorem be used to find the flux of F through S? Clearly answer yes or no, and then…

A: Given, F→=-9z,xexz-2xex2,12 and S is the portion of the plane 2x+3z=6 that lies in the first octant…

Q: A stationary proton is moved from point A, where the potential is 450.0 V,to point B, where the…

A: The work done by the electric force on a particle with charge q is calculated by the formula…

Q: QI Find dy for dx dt

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Q: Differentiate. y = e cos x + Cos( ex)

A: Given- y=ecosx+cosex To find- The value of the derivative of the above function. Formula used-…

Q: Find the principal unit normal vector to the curve at the specific value of the parameter.

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Q: What formulas are available for writing a moving object’s acceleration as a sum of its tangential…

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Q: Use Stokes' Theorem to evaluate curlF · dS, where

A: Let, F→=xyz , xy , x2yz. Stokes theorem states that ," Where C is the boundary of surface oriented…

Q: What is the relationship between Stokes’ Theorem and the Fundamental Theorem of Calculus?

A: Solution: Stokes Theorem: Stoke's theorem states that ''the surface integral of the curl of a…

Q: What are intermolecular forces? How do they differ from intramolecularforces? What are dipole-dipole…

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Q: Discuss in detail about Stokes’s stream function.?

A: Discuss in detail about Stokes’s stream function.

Q: Integrate f(cos x)e*+sin xdx B. e-sinx +C A. -et+sinx + C c. ettsinx + C D. e+sinx C

A: Note:∘ddx(sinx) = cosx ∘ddx(a) = 0                                         where a is constant∘∫etdt…

Q: um,0) =)0 sn So

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Q: Form first order diffential equation y=e^(siny+x)

A: Given equation is y=e^(siny+x)

Q: Describe the motion of a particle with posi- tion P(x, y) when x = 5 sin t, Y = 2 cost

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Q: (g) sin vt dt.

A: Intigrating the given equation.

Q: The Stokes' theorem states that: Ir = || (v-V)-n do True False o

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Q: J arcsin vc da

A: To evaluate the given definite integral.

Q: Integrate both sides dy = -dx

A: the given integral equation is                             ∫1y2dy=∫1xdx

Q: What is the physical significa

A: What is the physical significance of line integral of vector field?

Q: ■ Use Stokes’ Theorem to evaluate curl F dS

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Q: Describe the particle's acceleration

A: Given s(t) = t (2t - 1)2 and t = 2s The velocity v(t) = s'(t) = 12t2 + 1 - 8t The acceleration a(t)…

Q: Find the tangential and normal components of acceleration for F(t) =b cos ti +bsin tj + ctk

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Q: Sketch the velocity field V= in the first quadrant.

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Q: Differentiate the fol y = (sin x)(lnx) a)

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Q: 13. J sec0 de 14. J cot4x csc4x dx.

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Q: t sin (=) dt du

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Q: Define Gauss's theorem and Stokes theorem.

A: We will define first the Gauss's theorem then we will define the stokes theorem.

Q: Find the principal unit normal vector to the curve at the specified value of the parameter.

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.