dz where a inside r= C z-a 2ni

Q: fo axy dx + 2xy dy, where Cis the rectangle bounded by x = -1.x = 1, y = 1, and y = 5. 6xy dx + 2xy…

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Q: Ex. Evaluate ff y ds where S is the portion of the cylinder x + y = 3 that lies between z= 0 and z=…

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Q: J = fc cosh (z) dz, z2-3iz C: |z| = 1

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Q: e the triple integral: (x+y+z)dydxdz 6 24 18 12

A: Topic :- application of integration

Q: Find where 1)let . V°g r = l7| -- g(r) = In(r³) s = xi + yj + zk * vo x Vp 2) find = yz + zx2, P =…

A: Gradient and cross product

Q: u + c. Evaluate So (2x- y)3e dx dy with y = v, x= u-

A: To evaluate ∫02∫y22+y22x−y3eydxdy with y=v, x=u+v2.

Q: zl*dz, where C is x(t) t2, y(t) , t:2 1 Evaluate /=

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

Q: By algebraic substitution, the integral -dx is converted to: 4+. Vx 2ydy (A y+4 dy B y+4 y+4 D [vay…

A: Here is the solution

Q: D = {(x, y) E R² :0<x <∞, 0 < y<∞} olmak üzere, [ rye--v°dA D.

A: A multivariable function f(x,y) is a rule that is used to associate a number or quantity with a…

Q: 3xz dV where E: {(x, y, z) | 0 < r < 2, x < y < 2x, 0 < z < x + 3y} Evaluate E

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Q: his DE is variable separable. * (4ys-x) dx - 3y (y° + 2)dy = %3D O True O False

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Q: 3. Use Green's Theorem to evaluate J(* -6y)dx+(y +10y)dy where C is shown below.

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Q: Q.1B) If w = f(u,v) where u = tan-12 & v = In(x² + y²), the show that: %3D dw aw aw X +y 2- ax ду dv

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Q: (* +y – 4z) dV where E = {(x, y, z) | 0 < y < 2, 0 < * < y, 0 < z < a +y?} Evaluate

A: ∫y=00∫x=0y∫z=0x+y2x+y-4z dz dx dy Now, ∫z=0x+y2x+y-4z dz =x+yz-2z2z=0x+y2 =x+yx+y2-2x+y22…

Q: Q.1B) If w = f(u, v) where u = tan-12 & v = In(x² + y²),the show that: %3D dw aw aw +y- = 2 ax ду dv

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Q: Evaluate (z – i) dz where C:y(t) = VE² +1 + it³, 0<t < 1

A: We have to find ∫Cz-idz where C: γt=t2+1+it3, 0≤t≤1

Q: Obtain ∫C  ez / (z - πi) dz with C defined as z(t) = 4eit and 0 ≤ t ≤ 2π

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Q: 198). Let c be (,0) to(4r, 0,0) G=) ydx+ xdx t Xyz dz Is 6CX Y,Z) independent of C?

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Q: f(z) dz where a inside r= Z-a 2ni O 2nif(a) O 10

A: Using Cauchy integral Formula:

Q: 2) Determine dz/dx and dz/dy for z* – y? + x² = 6x²y³z? %3D

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Q: Ut for 0 <x <l u(x,0) = x u(0, t) = (1, t) = 0

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Q: dy where C is defined by dx + x2 + y? Evaluate x2 + y? C T(t) =,0 <t< 2n

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Q: Use Green's Theorem to evaluate ya dz – x dy where C is shown below. Left Half of (0,5) x*+y = 25

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Q: z)dy + (y -y of the triang Land (0 o 6)

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Q: u= In(x² +y² +='), x=rcos0, y =r sin 0, : =r= (1,0) =? O a. 1 O b. T/2 O .0 O d. -1 O e. 2

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Q: Find Vq if (a) =In (r) %3D (b) p= In (-) %3D We know r= /x² + y² + z2

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Q: m+n If x"y" = (x+y)*** m, n d'y prove that = 0 .2 dx?

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Q: Q.1B) If w = f(u,v) where u = tan-12 & v = In(x² + y²), the show that: %3D dw aw aw X +y¬ 2- ax ду…

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Q: dz Given z = e* sin y,x u? + v2,y = uv, find - dv %3D %3D

A: Here I am attaching image so that you understand each and every step.

Q: 10 dz where C2 is the top half C2 that is C2: |2| = 2 with z = re", 0 < %3D

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Q: Find Zy, Zxy , Z yx Z 3. = ax + cy+ C sin (X y) + d cus(y?) where a,b, c, d are Constant.

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Q: Evaluate SSS 2e(a²+y²+z?)"² dV over B where B= {(x,y, z) : x² + y² + z² < 1}. Take n = 3.

A: • The given region B has spherical symmetry, so it will be easy to solve this volume integral in…

Q: Evaluate cz dz, where c is |z| = 1 zG-2) Inz %3D

A: Let

Q: Evaluate: 3z dz when C: z = 0.5et (0 < 0 < T) %3D

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Q: find the dy リ=(メ+z)mx, (xを when 3In X

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Q: "ind where f(x, y, z) = e²´y and x = Vuv, y = ; %3D dv

A: To find the partial derivative using chain rule

Q: 1 dz where C is the cirlce z - 2=1.5. Evaluate : 4 1 C 8 Tti -8Ti 4 Tti

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Q: 3. Evaluate + y?)dV over the domain D contained between the two cylinders p = 1/2 and p = 3/2, for…

A: we know that volume in cylindrical coordinates are…

Q: find dw/dx, dw/dy, dw/dz using implicit differentation. Leave your answer in terms of x,y,z,and w.…

A: To find the implicit differentiation of the function: ln(2x2+y-z5+11w)=z...(1) So, take w as a…

Q: Find ∫C  ez / (z - πi) dz where C is defined as z(t) = 4eit and 0 ≤ t ≤ 2π.

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Q: dx dx is converted to: 4+Vx By algebraic substitution, the integral - 2ydy y+4 B y+4 © [ vdy y+4 dy…

A: Given, u= ∫dx/(4+√x) We can solve it by substitution method.

Q: Find . for (x,y) = x² + y² af af ду' дх Find ду' дх Je Je for f(x,y) : sin xy? x2+1

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Q: f f Find Af = where f(r, y) = In (9r2 + 5y2 – 3r). %3D

A: Here f is two variable function .To find ∆f , first calculate fxx and fyy then add them.To find fxx…

Q: dy Find at z da 2 and u = (2x + 1)ª. 0 given y = u + ·

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Q: | (yz? – y) dz + (z + 4) dy where C is shown below. 1. Use Green's Theorem to evaluate (-3,3) •…

A: Solution is given below..

Q: sin(r. r dr dy. Compute O y/3

A: To evaluate∫01∫y131sin(πx2)x2 dx dyx= y13y = x3

Q: 16. f(x, y, 2) = y - Vr? + z?; P(-3, 1, 4); a 2i-2j-k

A: To find the directional derivative of f at P in teh direction of a So, given f(x,y,z)=y-√(x²+z²);…

Q: Use Green's Theorem to evaluate |. (y? – 6y) dx + (y³ + 10y²) dy where C is shown below.

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