Q (3): Given the field D = p sin 0.5o a, + p cos 0.50 a, +pa, C/m, evaluate both sides of the divergence theorem for the region bounded by 0 Sps1,0SOSa2,0sz52.

Q: Q1: Evaluate: 2x dV where E is the region under the plane 2x + 3y + z = 6 that lies in the first…

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Q: Q2. Evalnate the double integral SS хе ク over the finite regieon 2 R={(x)): x2, y54ーx3

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Q: (d) Let P = xy², Q = x²y and C denote one petal of the four leaved rose defined by r = -450<.…

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Q: 3.4.13 Verify the divergence theorem [[ F. JS = [] F.dS div F dV S for F = 4xi-2y²j+z²k over the…

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Q: 43.) Show by checking cross partials that F = (4x³y² – 2xy³, 2x*y – 3x²y² + 4y³) is conservative Use…

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Q: Evaluate the line integral along the given paths. | xy ds (a) C: line segment from (0, 0) to (5, 4)…

A: We need to evaluate,                          . For (a), .

Q: In the following case, a region D is defined. Tell whether the region is a domain. If it is a…

A: The region D here is all of R3 except the z axis i.e D=[(x, y, z) such that x2 + y2 &gt; 0] clearly…

Q: The approximation of the integral -2) In (x+2)dr using the two points Gaussian quadrature மாmua is)

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Q: Q1. Verify Divergence theorem for the function F = ēpp over the semi-cylindrical volume x2 + y? < a…

A: Given:- →F=→eρρ V=x2 +y2≤a0≤z≤h,x≥0

Q: Consider the improper integral and the propositions dx J = = 6of foo x² + 3 1- The integral J…

A: Find out the correct statement.

Q: D3.9. Given the field D = 60 sino ap+1.5p cosa, C/m², evaluate both sides of the divergence theorem…

A: Given the field  D=6ρsin12ϕaρ+1.5ρcos12ϕaϕ and the region bounded by ρ=2, ϕ=0, ϕ=π, z=0, z=5

Q: Use the Divergence Theorem to evaluate ff F-n do where S F(x, y, z)=(x² +cos yz, y-e², z² + x²) and…

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Q: 1. Evaluate the line integral of E-xa, -y a, along the segment P; to P; of the circular path as…

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Q: 2. Find an asymptotic expansion of the solution y(x) to leading order that is valid on [0, 1] for…

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Q: 1 Use the Cauchy integral formulas to evaluate the e cos z *zp- 22(2: - 37) where C is the region…

A: Given: Let  I =∮C  eiz cos zz2 2z-3π dz  .....1 And,  C is the region covered by circle z-2=3.

Q: Given F = (2xze*²z – 4, cos z, x²e*z – 3ycos?z sin z) 1. You are to show that the line integral S.…

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Q: 2. a) Compute the integral fa f(x) dx using 5 point composite rectangle, trapezoid and Simpson rules…

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Q: The Fourier integrals of two continuous functions f(x) and g(x) defined on R are given by sintwa] 2л…

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Q: the potential function f for the field F = 5x i + 9y j + 4z k. eral expression for the infinitely…

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Q: Verify Gauss Divergence Theorem for F = xy²î + yx²j+ek for the solid region D bounded by z = √x² +…

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Q: Q3. Verify the divergence theorem for F = 3 i+ xy j+x k taken over the region bounded by z = 4 – y?,…

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Q: 5) S, is calculated by the thorem of divergence of the full range straight flux F(x, y, z) = 2xỉ +…

A: Given: F(x, y, z) = 2xi + y + zk along, almost every where with z = x² + y² paraboid and z = 2x…

Q: If D = 15p sin 2øa, + 10p² cos 2pa, C/m², evaluate both sides of the divergence theorem for the…

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Q: 149. sin x cos ydx + (xy + cos x sin y)dy, where C is the boundary of the region lying between the…

A: We have to find ∫c sin x cos y dx +(xy+cos x siny)dy , where C is the boundary of the region lying…

Q: b) Use the divergence theorem to compute ff, F ñ ds, where S is bounded by x+ y + 2z = 2 located in…

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Q: Obtain the circulation integral of the field F = xyî + y²ĵ in the curve C defined by the boundary of…

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Q: 5) S, is calculated by the thorem of divergence of the full range straight flux F(x, y, z) = 2xỉ +…

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Q: Given the field D = 6sin 0.50 a, + 1.5p cos 0.50 a, C/m². Show the divergence theorem is true for…

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Q: 6p sin oa, + 1.5pcos oa C/m², evaluate both sides of the divergence theorem for the region bounded…

A: Solution :-

Q: Q4) Use the Jacobian to evaluate ( sin (x +3y) xdy where 1+(x - y) 2 is the region enclosed by: x…

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Q: Given i = x²& + xy ŷ + yz 2 check the fundamental theorem of divergence over a cube whose each side…

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Q: Obtain an asymptotic expansion for I(z) = S e-zy*/2 cos y² dy, as z → 00 along [0, 0).

A: Here, we need to find an asymptotic expansions for I(z)=∫-∞∞e-zy22cos y2dy, as z→∞ along [0, ∞). We…

Q: What is the value of the line integral on the field 5a² y F(x, y) = () i + 5æy? 2 2 along any path…

A: The given field is Fx,y=5xy22i→+5x2y2j→. Consider the function fx,y=54x2y2. Now,…

Q: Given the field D = 6p sin 124 ap +1.5p cos 12 a, C/m2, evaluate both sides of the divergence…

A: field D=6ρsin12ϕ ap + 1.5ρcos12ϕ aϕ C/m2 here ∇ = aρ ddρ + aϕddϕ+azddz Divergence = ∇·D ∇·D=…

Q: (1) Let F(x, y, z) = (1, 2yz², 3z² + 2y²z). (a) Find the divergence of F (b) Show that is…

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Q: Express the given integral f, 2x dx as the limit of Riemann sum. a. 2x dx = lim E-(1+) G+1)* E- d.…

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Q: integrate ƒ over the given region. ƒ(s, t) = e^s ln t over the region in the first quad-rant of the…

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Q: 12/ Vse the divergence of the fleld FCX4,22= a (e,3yt sin liz),9zt²+]y through the Surfacé theorem…

A: To Determine: use the divergence theorem to evaluate the flux of the field…

Q: Find. the diveraence. and.cur.l.4the fallown Vecter. field: ..F= Xe..y.e. k.

A: As per guidelines if multiple questions are posted we are allowed to solve only 1st question....

Q: 1- Find integral result for f f e**+* dydx, where R the semicircular region bounded by the x-axis…

A: (1) We have to find the integral ∬Rex2+y2dydx, where R is the semicircle region bounded by the…

Q: Let z= 28x + 32xy - 8y , where x(t,s) = cosh (4t) cos (5s) and y(t,s) = sinh (4t) sin (5s). ze at…

A: Here, z=28x2+32xy-8y2

Q: 53. Verify the divergence theorem for A = 2x?y i – y² j + 4xz2 k taken over the region in the first…

A: Given : A=2x2y i- y2j + 4xz2 kbounded by y2+z2=9 and x=2

Q: 7. Use the divergence theorem to find the outward flux of F= 3xy²i+ xe² j+ z° k across the boundary…

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Q: use Greens Theorem to evaluate . cosy dx + (xy- x siny)dy Ewhere C is the bounday of the y Jx,…

A: We have to evaluate given integral using Green's theorem.

Q: 4. Use the Divergence Theorem to evaluate the flux integral JS, F-ndA over the surface of a…

A: Given that, F=(3xy3z5,3y,-xy3z6)F⇀=3xy3z5i^+3yj^-xy3z6k^ We have to evaluate the integral  ∫∫sF⇀.ndA…

Q: 12/ Vse the divergence theorem to evalvate the flux ef the fleld FC,22= a (3yt sin l2),9z+?+9y²…

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Q: Set up the iterated (triple) integral for the integral ]]] xy¹z³ dV where S is the tetra- S hedron…

A: We will find limits of variable and then find value of integral

Q: Compute the integral ∮C [(cos x − 3y) dx + (2x − sin y) dy], where C is the closed curve that…

A: The region of integration C is divided into three line segments C1, C2 and C3. Let C1:y=0,…

Q: 2. We have seen that the FTC for line integrals implies fc Vf - dĩ = 0 for any smooth closed path C…

A: FTC for line integrals implies ∫C∇f·dr→=0 for any smooth closed path C and any smooth function f (a)…

Q: If D = 10 ρ2 sin2φ aρ + 8 ρ2 cos2φ aφ C/m2 for the region 2 < ρ < 4, 2 rad < φ  < 4 rad, 1 < z  < 2.…

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