1. Calculate the integral |- z+i dz throughout the contours C: z' + 2z? a.) |z +2-i|=2; b.) |z – 21| = 1 ; c.) |=| = 3 ; d.) |z -1=2

Q: Please solve the line integral Se F · dĩ In where: F = y²i+2r(y+1)j Is along 2 unique paths from the…

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Q: 6- Evaluate the line integral fe F dr, where F = [ry, yz, r2] and C is the boundary of the…

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Q: Use Green's Theorem to evaluate the line integral v+e*) dx + (6x+cosy) dy where C is the triangle…

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Q: Prove that fe, r*dx + rydy = 0 where Co is the line segments from (0, 1) to (0,0) by using…

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Q: Use Green's Theorem to find the line integral. C is to be traversed in the counterclockwise…

A: In the question it is asked to calculate integral using Green's Theorem.

Q: Compute the line integral of F over C. (a) F = (,-1, In x) and C is the line segment from (, 4, 2)…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: .Find the exact value of the double integral. J (2x + 5y) dA, where R is the rectangular region…

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Q: Compute the line integral ∫_C F · dr, where F (x, y) = 〈−x^3, xy〉 and C is part of circle x^2 + y^2…

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Q: A solid G is bounded by the paraboloid z = 4 - x? – y?, the cylinder x² + y? = 4 and the plane z =…

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Q: Let C:z|=1 in the counterclockwise direction and I = $. dz, J = f. Lnzdz, and K = $. tanzdz. For…

A: We can apply cauchy Goursat theorem on I and K but not on J

Q: + y^5)dy] where C is the unit circle x^2 + y^2 = 1 traversed counterclockwise.

A: we have to compute the given integral ∮x5+y3dx-(x3+y5)dy     where C is unit circle x2+y2=1.C

Q: Prove that the integral of the bottom of a half ellipsoid, (x/a)^2 + (y/b)^2 + (z/c)^2 =1, is equal…

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Q: Let R be the trapezoid with vertices (1,-1), (3,3), (3,-3) and (9,9). Give a change of variables to…

A: Given that ,  R be the trapezoid with vertices (1,-1) , (3,3) ,(3,-3) and (9,9) . Let , the vertices…

Q: a) Evaluate the line integral TM UTM in terms of 7 where F = cos yi+ rj + ye*k and C is the line F…

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Q: A solid G is bounded by the paraboloid z = 4 – x2 – y², the cylinder 22 + y? = 4 and the plane z =…

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Q: Evaluate the triple integral ||//. z°e" dV where E is bounded by the parabolic cylinder z = 16 – y?…

A: The volume of a solid can be calculated using the triple integrals. The unit dV can be written as…

Q: Q:4) Use Green theorem and evaluate the line integral ${Mdx + Ndy} Where M(x,y)=y², N(x,y)=x², C is…

A: See the details solution in below

Q: Use Greens Theorem to evalua te the line integral Sr -93 dx +x*dy. where C is the positively onented…

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Q: 22. Compute the contour integral (Баллов: 2) Sof (2) dz, z E C, if f (z) = and path is semicircle z…

A: Topic:- application of integration

Q: Y – 5x |dA x + y 100 cos

A: We have to evaluate the double integral ∬ 100cosy-5xx+ydxdy over the region D where D is the…

Q: A- Find all values of z such that sinh(z) = B- Are |z, Img(z) analytic? Give reason. C- Choose the…

A: We have to solve the given questions

Q: Verify Green's Theorem by evaluating both integrals aN v? dx + x² dy | dA ду ax for the given path.…

A: Given problem:-

Q: 1. Evaluate the integral: SSf, xe**+y<+zt dV where B is the portion of the unit ball x² + y² + z² <…

A: Here, the region B is the portion of the unit ball x2+y2+z2≤1 that lies in the first octant.…

Q: Evaluate the triple integral. 6xyz dV, where T is the solid tetrahedron with vertices (0, 0,0), (1,…

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Q: Use either form of Green's Theorem to evaluate the following line integral. $9x²1² 6 C $9x³y² dx +…

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Q: (a) Find the line integral of f (x, y, z) = -x + y + z over the straight-line %3D segment from (1,…

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Q: Use Stoke's theorem to compute the integral SL(V × F) · n dS, where F(x, y, z) = (xz, yz, xy) and S…

A: We have to compute ∬(∇×F)·n dS , where F(x,y,z)=(xz,yz,xy) and S is the portion of the sphere…

Q: - Prove that the contour integral – z)dz = -12i where C is the triangle with points 0, 3i and -4…

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Q: Given F(x, y, z) = (z, x, y). Evaluate the line integral of F along the positively oriented boundary…

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Q: Find the line integral of F= 2√zi-4xj + 3√√yk, from (0,0,0) to (1,1,1) over each of the following…

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Q: Use the residue theorem to calculate the contour integral |z|=5 dz. /zl=5 (z + 1)²(z + 2i)

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Q: Use Green's Theorem to evaluate the line integral Lv+e) dx + (3x+cosy) dy where C is the triangle…

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Q: Evaluate the triple integral. SSS 5x²e" dv I where E is bounded by the parabolic cylinder z = 1 - y²…

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Q: Let C be the positively oriented square with vertices (0,0), (3,0), (3,3), (0,3). Use Green's…

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Q: Compute the contour integral dz, where l'is the contour of the perimeter of the square with vertices…

A: We will do it  by dividing r into 4 paths.

Q: 21. (y² dx + x² dy)

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Q: 2. Evaluate the given line integral, (-y, x – y) · dR, where C is the line segment from (2,0) to (0,…

A: Using parametric equation, line integration is evaluated.

Q: Use Stoke's Theorem to evaluate the line integral / 7ydx + 3zdy + dz where C is the intersection of…

A: Use Stoke's Theorem to evaluate the line integral ∫C7y dx+3z dy+ dz, where C is the intersection of…

Q: Evaluate the line integral ScF- dr where F(x, y) = (5x + 4y)i + 3xyj and C: r(t) = 3ri + rj, 0sts1 O…

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Q: Use Cauchy's Integral formula to evaluate the integral: Sa (z+1) e2z dz where C is a circle |z| = 3.…

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Q: Compute the line integral f, x?dx + y²dy where the path C consists of the arc of the circle x? + y?…

A: Here we solve the given problem of integral.

Q: Use the Cauchy integral formulas to evaluate the eiz cos z dz, 2²(2z – 37) where C is the region…

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Q: Does the integral of f(x, y) = 1/(1 – a² – y²) exist over the disk a? + y² < 1? Explain. -

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Q: Use Stokes' theorem to evaluate line integral (z dx + x dy + y dz), where C is a triangle with…

A: Consider the provided question, We have to evaluate the given integral by using the stokes theorem,…

Q: Evaluate the line integral Levis where C is the half circle x² + y² = 1, y ≥ 0. x² + y² ds

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Q: Use Green's Theorem to evaluate the line integral  ∫c (y-x) dx + (2x-y) dy for the given path. C:…

A: Given data-    The line integral -                          ∫c (y-x) dx + (2x-y) dy .    We have to…

Q: 5) Using Green's theorem, convert the line integral .(6y? dx + 2xdy) to a double integral, where C…

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Q: Use Green's Theorem to evaluate S. axy dy + cxy dy, where C is a counterclockwise oriented…

A: Given : a=2, c=8 We have to use Green's Theorem to evaluate            ∫C axy dy+cxy dy where C is a…

Q: Evaluate the line integral F dr, where C is given by r(t) = (t², t, vT), 0<ts2 and (x, y, z) = (z,…

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Q: Use Green's Theorem to Calculate the Line Integral ſy²dx + x²dy, where c is the triangle o vertices…

A: Given that, the line integral is ∫y2dx+x2dy and the vertices of the triangle is 0,0,4,0 and 4,4. By…