use Greens Theorem to evaluate . cosy dx + (xy- x siny)dy Ewhere C is the bounday of the y Jx, traced in the counterclockwisc dieohion. rogion bounded by you and

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A: The Stroke's theorem is ∫CF.dr=∬Scurl F.n dS Here n=3k. ∫Csinz dx-cosx dy+siny dz=∫0π∫01curl F.3k dy…

Q: Evaluate the integral O 03/20 Ⓒ100 C 87² dx using the two-point Gaussian quadrature rule. 1+16z4

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A: Here we have to evaluate the given double integral where T is a triangle with vertices…

Q: Evaluate the iterated integral: a S " cos(2) dy dar.

A: Given that the double integral

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A: We have to evaluate the integral ∫−3311+x4dx by using two-point Gaussian quadrature rule. Here,…

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

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A: See the attachment

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

A: Find out the correct statement.

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Q: Calculate the volue of the de integral 23 - 1 2 F soro fallowing c a) Cil2+1|= 1 Curves. 6)…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 3.1 Use the Cauchy integral formulas to evaluate the e cos z I. 7(2: – 3m) where C is the region…

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Q: Evaluate the integral (6x-y)dx + (x+6y)dy along the path C, defined as y = 16-x² from (0, 4) (4, 0).…

A: Answer: The solution is given below:

Q: Verify Green's Theorem by evaluating both integrals v² dx + x² dy = / / dA ax for the given path. C:…

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Q: Find the particular intengral of the following ODE d2y/dx2 + 9y = cos 3x

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Q: Verify Green's Theorem by evaluating both integrals ax dA ду for the given path. C: rectangle with…

A: From: (0, 0) to (5, 0)y=0, dy=0∫ y2 dx+ x2 dy =0From: (5,0) to (5, 9)x=5, dx=0∫09 x2 dy= ∫0925…

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: Evaluate the integral S CO|CT CT | CO CT /Co NIC 8 dx using the two-point Gaussian quadrature rule.…

A: We have to evaluate the integral ∫−22816+x4dx using the two-point Gaussian quadrature rule. Here,…

Q: Find the product of the integral 1- S x²cos(xy)dxdy

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Q: H.W: Evaluate the integral 3. -4y)dydx x*ydxdy 1 -1

A: ∫xndx=xn+1n+1

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A: Topic:- integration

Q: Let E be the solid that lies under the the plane z = 4, and on the xy-plane it is enclosed by y=…

A: Find your answer below

Q: Consider the following line integral. xy dx + x²y dy, Cis counterclockwise around the triangle with…

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Q: 2. Use the Definition of Residue to show that: dz -ni 3 Izl=1z sinh z Where u> |z| > 0

A: Prove,∫z=1dzz2 sinh z=-πi3 ∫z=1dzz2 sinh z=∫z=1fz dz .........equation 1 fz=1z2 sinh z , 0&lt;z&lt;π…

Q: to find 2y dx-xdy, Use where C is the green's theorem the the eircle wi'th radivs 4 Centered at…

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Q: Verify the Green's theorem for the following integral $. sinydx + (x – cosy) dy where curve C is the…

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Q: Find the particular intengral of the following ODE d2y/dx2 +4y = sin 2x

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Q: Verify Green's Theorem by evaluating both integrals √< y² dx + x² dy = [] (ON - 3M) de dA ?х ду for…

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A: Solution is given below:

Q: Verify Green's Theorem by evaluating both integrals dA [_v² dx + x² dy = [ ] (ON-OM) DA ду for the…

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Q: 1. Evaluate the integral |// cos (-) dV, where G is the solid defined by the G inequalities <y< , y…

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Q: Evaluate the integral. cos(6 z) dz %3D

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Q: Evaluate the following integrals (taken anticlockwise) using Cauchy's theorem: (f) P.„(²+1)² eiz dz…

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Q: Find the diih of y integral tanar 230 e dn dy a) | shso b) c) O sysl-z 1-2 d) Nove of theoe

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Q: Verify the Green's theorem for the following integral O sinydx + (x – cosy)dy where curve C is the…

A: Answer

Q: (b) Let F(x,y) = (e2*y+cos(7x²), xºy^+e>Y³} Use Green's Theorem to set up the line integral F. dr as…

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Q: Find the value of the closed loop integral z3 + sin z -dz (z – i)3 taken around the boundary of the…

A: GIven  ∮z3+sinz(z-i)3dz   To compute this integral we have to use the following theorem. Theorem:…

Q: d. Dse the bosic properhes of integrC followng theorem. THEOREH:If (Cx. Y) = FG)G(), wbe La,bland G…

A: We will use dominated convergence theorem to prove the given theorem.

Q: 7. Prove that the SolutmM of y + y = o is B sinx (hint y= Xu) by using Bessel's Functron definstian…

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Q: 1) If f(x)=x2, find f(x+2)-f(2) .what is bijective h mapping? 2) Does the integral J, dx exist?

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Q: Verify Green's Theorem by evaluating both integrals ON [ v² dx + x² oy - [√(x 0 ) A dy = dA JR əx ду…

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Q: let us efine fn enj-S (n) = otherwise b) we wo ld like to calco late the lebesgue integral Sf dm…

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Q: Evaluate the improper intergal 1 dx using the residue (x² + 1)3 theorem.

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Q: determine the area inside of the inner loop of the limaçon r = 2 cos 0 – 1.

A: We have to find area of r= 2cos(theta)-1

Q: Let E be the solid that lies under the the plane z = 4, and on the xy-plane it is enclosed by y =…

A: