Find the laplace Sf fhe fanction: ft)esint u lt-) )= where ult- T) is aunit | tunction fur

Q: Let F = Use Stokes' Theorem to evaluate · dī, where C is the curve of intersection of the parabolic…

A: To find the curl , ∇×F=i^j^k^∂∂x∂∂y∂∂zxy5z7y=i^7-5-j^0-0+k^0-x=2i^-xk^ To find the normal vector,…

Q: O Calcalate the integea/ over the giren region by dhangng to polar cocalinater fcx,y) = 14xy/;

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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 line integral C ydx + zdy - 2xdz; where C is the helix r(t) = costi+ sin tj+tk , 0 <= t…

A: To evaluate the given line integral.

Q: Find the area of the surface of revolution r(u, v)= 6sin(u)cos(v)i+ 6uj+6sin(u)sin(v)k, where 0SusT…

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Q: Evaluate the line integral, where C is the given space curve xeZ ds, Cis the line segment from (0,…

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Q: Selve e the differentsal Equedon. y) = 1 , ylo)=2 Laplace Fransform using

A: Take Laplace to transform throughout the given ODE Ly''+25y=L10cos5t-2sin5t apply the differential…

Q: Let F = < rY, 3z, 4y Use Stokes' Theorem to evaluate | F . dī, where C is the curve of intersection…

A: Here we have, F→=xy, 3z, 4y Using the stoke theorem, we have to evaluate the ∫CF→·dr→=? Where C is…

Q: Let F = Use Stokes' Theorem to evaluate F dī, where Cis the curve of intersection of the parabolic…

A: Given F¯=xy,4z,6y We have to evaluate ∫CF¯⋅dr¯ by using stokes theorem, where C is the curve of…

Q: Use spherical coordinater to set up the integmal SzdV, the integral SSSz dV, where Q lies between…

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Q: Use the Divergent Theorem to find the outward flux ofF = yi+3yj+ 322k across to the boundary of the…

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Q: Use Stokes' Theorem to caleulate ſ. F - dř, where F = zyi+3=3+5zk, and C is the closed path around a…

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Q: Use Stokes' theorem to evaluate (ry – y) i – In zj+ (r+r²) k) - dr, where C is the intersection…

A: Let F be a vector field and C be the boundary of the surface S. The Stoke's theorem states that…

Q: Find the arclength of the portion of the Helix F(t) = (3sin(t), 3cos(t), 4t) that lies insıde the…

A: Given eqn. of Helix r→(t)=3sint, 3cost, 4t and Sphere S={x,y,z x2+y2+z2=153}

Q: State two other forms for the line integral ∫C F ⋅ n ds given that F = ⟨ƒ, g, h⟩ .

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Q: Find the curvature of the plane curve with equation y (x, f (x)) on the curve, by using the…

A: We will find out the required value of curvature .

Q: 21. r(t) = t³ j + t² k %3D

A: Given  r(t)=t3j+t2k

Q: Suppose F(x,y)=4yi +3xyj. Use Green's Theorem to calculate the circulation of F around the perimeter…

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Q: Assume that the density of the cone is ρ(x, y, z) = k√x2 + y2 and find the moment of inertia about…

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Q: Evaluate the cylindrical coordinate integral: L L dzr dr de O 647 O 87 O 167 O 1287

A: To solve the integral

Q: Let F = . Use Stokes' Theorem to evaluate curlF · dS , where S is the hemisphere x? + y? + z2 = 9,…

A: Given that, F=x2eyz,xexz,z2exy Given hemisphere that S:x2+y2+z2=4,z≥0 From stoke's theorem, ∬Scurl…

Q: The inverse Laplace hransform F(s) = 31 + Inci2-s)-nc19-s) is of %3D

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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: Use parametric to solve

Q: Consider the parametrization y: [0,47] → R, (t) = (t cos t, t sin t), of a counter-clockwise spiral…

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Q: Show that if u is a unit vector, then the arc length parameter along the line r(t) = P0 + t u from…

A: It is known that,

Q: Let F(z, y, 2) = 12?ri + (ty + tan(z))j + (1z?z+ 4y?)k. Use the Divergence Theorem to evaluate f, F…

A: We must apply the Divergence theorem on a closed solid, but the surface S is not closed (it is just…

Q: Let F = . Use Stokes' Theorem to evaluate / curlF · d5, where S is the hemisphere x² + y² + z² =…

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Q: Compute the flux of F= xi+yj+ z*k across the cone z =Vx2 + y? , 0szs1, in the downward direction.…

A: We have to find the flux in the downward direction.   Let us assume that x=rcosθ, y=rsinθ, z=r Then…

Q: b. Describe the rigid motion(s) that would map AUVT onto ASVR.

A: Triangle SVR is congruent to triangle UVT by SAS congruence rule as per a. part. Four types of rigid…

Q: Utilice las propiedades, los teoremas y las tablas de la Transformada de Laplace para encontrar la…

A: The given differential equation is  y' + y = tsint,      y(0) = 0

Q: Compute the flux of F = (r, y, z*) across the cone z = x2 + y?, %3D 0<<1, in the downward direction.

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Q: Let F = . Use Stokes' Theorem to evaluate curlF · d§ , where S is the part of the paraboloid z…

A: Given: F=-yz,xz,xy To Find: Use Stokes' Theorem to evaluate ∬Scurl F·dS, whereS is the part of the…

Q: Evaluate the line integral F. dr, where F(x, y, z) = 4xi + 4yj – 5zk and C is given by the vector…

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Q: What is the differential for the total surface area of a frustum of a cone with i as the slant…

A: The formula for total surface area of the frustum of the cone with the given slant height l is Total…

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: Let F = Use Stokes' Theorem to evaluate F. dī, where C is the curve of intersection of the…

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Q: Use Green's Theorem to calculate the circulation of F =2yi +xyj  around the unit circle, oriented…

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Q: Evaluate the line integral fx ds between (4,0) and (0,4), where C is the circle of radius 4 centred…

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

A: Given function is  F=x2eyzi+xexzj+z2exyk    (i) S is the hemisphere x2+y2+z2=16 , z≥0 oriented…

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: If F=xi+yj, prove that JF.ñds equals [V.FdA, where R is the disk of radius C R "a" and centre at the…

A: Given Data: F =xi  +yjTo Prove:∫C F . n ds =∫R∇·F dA where R is the disk of radius ''a'' and centre…

Q: Let F(r, y) = 4xî + 3yî and let i be the outward unit normal vector to the positively oriented…

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Q: Exercise 7 T. Given: SU and RT bisect each other a. Prove: ASVR = AUVT b. Describe the rigid…

A: Given: A quadrilateral STUR, where SU and RT bisect each other. a. Since SU and RT bisect each…

Q: Evaluate the contour integrals cosh z dz 4z2 + 72 z +1 dz 223 – 322 – 2z and around the unit circle…

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Q: Let F = · Use Stokes' Theorem to evaluate curi curlF · d§, where S is the part of the paraboloid z…

A: here i had written stokes theorem and done some basic calculation to find the curve of intersection…

Q: Use Stokes' Theorem to evaluate |/. CurlF dS, where F(r, y, 2) = xyzi + xj + e" cos zk and S is the…

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Q: Compute the arc length function L = | ||r(u)||du for r(t) = (16t1/2, In(t), 32t), and a = 1. %3D %3D…

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Q: Show that the circular helix r(t) = (a cos t, a sin t, bt), where a and b are positive constants,…

A: The equation of the given circular helix is rt=acost, asint, bt where a and b are positive…