5. Using Divergence Theorem, calculate the integral // ry dx + yz?dy + za*dz where S is the upper hemisphere given by x² + y? + z? = 25.

Q: 2. Give iterated integrals for (xz*)dS where S is the part of the cylinder x² + y = 9 above the…

A: Given that x2+y2=9 and the part of the cylinder which is above XY plane implying that z > 0. We…

Q: 9) Use Fubini's Theorem to compute the double integral ƒƒ_ƒ(x,y)dª_where…

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Q: Find the line integral of x ds over C where c is the line segment from (1,0) to (0,1) using two…

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Q: Prove that: I = , Cos () dxdy = sin(1) 2 where R the region bounded by x + y = 1,x = 0,y = 0

A:

Q: Evaluate the line integral, where C is the given cu curve. (x + yz) dx + 2x dy + xyz dz, C consists…

A: C consist line from A (2, 0, 1) to B(3, 3, 1) Now,

Q: ON Verify Green's Theorem by evaluating both integrals 7y dx + 7x*dy = J J]a дм ƏA for the path ду…

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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: Let S be the portion of the cylinder z = 1 − x2, in the first octant and between the planes y = 0…

A: The required surface is shown below: Note: If the surface is given by the function z=f(x,y), then,…

Q: Use Green's Theorem to evaluate the line integral (y - x)dx + (2x - y)dy

A:

Q: Use Green's Theorem to evaluate the line integral. 2xy dx + (x + y) dy C: boundary of the region…

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Q: Evaluate the line integral, where C is the given curve. (x + 8y) dx + x2 dy, C consists of line…

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Q: dz where C:|z – 2| = 0.2 (z – 2)³(z – 5) by using (a) Cauchy's integral formula

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Q: 3. Sketch the region and evaluate the iteraterd integral (a²y – ry?)dydx. 2.0 1.5+ 1.0 0.5 0.0 0.0…

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Q: Apply Green's Theorem to evaluate the integral (-5y² dx-5x² dy), where C is the triangle bounded by…

A: greens theorem

Q: 5. Using Divergence Theorem, calculate the integral /| ry dx + yz²dy + za²dz S where S is the upper…

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Q: Evaluate the integral (ycoS z + 1) dydz.

A:

Q: Evaluate the line integral Say dx +z dy, where C is the line segment from (-1, 1, 2) to (2, 3, 1).

A: Evaluate the line integral ydx +zdy where C is the line segment from (-1,1,2) to (2,3,1). Here i…

Q: Evaluate by Gauss divergence theorem for |] 4xz dy dz - y dz dx + yz dx dy S Sin tho a

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Q: 4. Compute the integral x sin (xy) dA where R is the region 0 <x <1 and 0<y < .

A:

Q: Evaluate the double integral. [[ ×20 (2+2y) dA, D is bounded by y = x, y = 2³₁x20

A: off

Q: valuate the double integral. SL,(6x + 3y) dA, D is bounded by y = VT and y = r²

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Q: Solve for the area of the portion of the cylinder x = /1 – y², which lies between the planes z = 0…

A: Here is the solution of the given problem:  By using line integral to find the surface area of…

Q: Sketch the curve ĕ= E Set uf, buz de not evaluale, an integral for the are- length of the Rurve from…

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Q: 2. Evaluate the triple integral where E is the solid bounded by y = 2x² + 2z² and the plane y = 8.

A: A detailed solution is given below.

Q: 3) Show that the line integral is independent of path and then evaluate the inte S, sin y dx + (x…

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Q: Determine the integral of x y dx dy. Use inner limits=0 to (y + 1) and outer limits=0 to 1.

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Q: 3) . (3x2 — Зуz+ 2xz)dx + (3у? - 3xz + z?)dy + (372 — Зху + х? + 2yz)dz Calculate the curvilinear…

A: Let's find.

Q: Find the areas of the regions 1. Bounded by the spiral r = 0 for 0 < 0 < T r = 0 2'2 х (п, т)

A:

Q: Compute the line integral of f(x)=2x over the curve y=x^2 from (0,0) to (1,1)

A: Given query is to find the the line integral for the y = 2x over y = x2.

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

A:

Q: Calculate the double integral S TR (2x + 8y + 16) dA where R is the region: 0 < x < 4,0 < y < 1.

A: we have to find the double integral  ∫∫R(2x+8y+16)dAwhere R is  the region 0≤x≤4,0≤y≤1

Q: Find the line integral of f(x,y,z) = -x + y+z over the straight-line segment from (1, 2, 3) to (0,…

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Q: Use Green's Theorem to evaluate the line integral. J. 2xy dx + (x + y) dy C: boundary of the region…

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Q: Set up UP the integrel the Pegioni Th bounded 2x2 and y =l+ x F(x,y) dA in by: y= 2x? 2. 4.

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Q: 4. Use Green's Theorem to evaluate the line integral: f ye dx + x*y² dy, where C is the from (-2,0)…

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

A: Use greens theorem

Q: Calculate the double integral / Rx cos(2x + y) dA where Rl is the region: 0 <x<,0 < y< 6. 2

A: Here we have to find the value of double integral.

Q: Evaluate the integral using integration by parts. Scot-¹(8y)dy 1 Scot ¹(8y)dy = -x In (cos (6y)) + C

A: The given integral,       ∫cot-18ydy

Q: Use Green's theorem to evaluate the integral: 6(-x²y)dx + xy°dy where C is the boundary of the…

A: Let C be a positively oriented, piecewise smooth, simple, closed curve and let D be the region…

Q: 3. Use the change of variables: u = x + y , v = y – 2x to evaluate the integral: Cx+y(y-2x)²dydx .…

A: Given: The change of variables: u=x+y and v=y-2x We have to evaluate the integral: ∫01∫01-xx+y y-2x2…

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

A: Green's theorem: ∫CMdx+Ndy=∫∫R∂N∂x-∂M∂ydA   Given: I=∫Cy-xdx+2x-ydy and C: y=x and y=x2-2x It means…

Q: 10.Calculate the double integral ffRXsinydydx, where R is bounded by y=0, y=x2, x=1.

A: Fubini's Theorem- If f(x, y) is continuous over the region R defined by a≤x≤b,   c≤y≤d then,…

Q: 1- Integrate The furction F(X,y= over The region bounded byrj=X7y=2x9 x =1/X=?

A: According to our company guideline if multiple questions are posted we must do only first. You can…

Q: Evaluate the double integral. 7x cos(y) dA, D is bounded by y = 0, y = x2, x = 7 %3D

A:

Q: 2. Use the Fundamental Theorem of Line Integrals to evaluate fe F.dR, where F(x, y) = (x²y? –…

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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: dl /x² + y² + 4

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Q: Evaluate the iterated integral: 1 IIT 24a*yz² dz dy dz

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Q: 8) consider the region R in the first quadrant(xz0, y2) bounded by x=2y² X=Y²+1 a) set up, but clo…

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