If F(x, y, z) = 10yzi + 10xzj + 10xyk, find div F and curl F. div F =

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A: Given: ∫02∫02z∫y2ydxdydz

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Q: Suppose F(z, y) = zyi+ (# – y)j and C is the triangle from (4, 0) to (-4,0) to (0, 4) to (4,0). (a)…

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Q: Q0 Integrate 2 from x? o to L x²_2 trapezaidal rule with four

A: SolutionIntegrate x2-2 from 0 to 4using the trapezoidal rule with 4 bandsFormula of trapezoidal…

Q: Evaluate the double integral. |/ (2x + y) dA, D = {(x, y) | 1 < y< 4, y – 3 < x :

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Q: raluate the double integral R 3ædA where Ris the triangle with vertices (-1,0), (0,1) and (1,0).

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Q: Evaluate the line integral -ydr + rdy along the curve C : y² = 6x from (6, 6) to (0,0). NOTE: Enter…

A: The given line integral is ∫c-ydx+xdy along the curve c: y2=6x from (6,6) to (0,0)

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Q: Calculate line integral F-dr where F(x, y) = (7x + y, 5x + 2y) and C is a rectangle with vertices…

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Q: Evaluate the double integral. (2x + y) dA, D = {(x, y) | 1 < y< 2, y – 1 < x < 1}

A: Double integration

Q: Q1) Find plane area bounded by y = 2,y = 6 – x, and y = 8 - 3x using double %3D

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Q: Solve the DEs by LT. please show complete slution.   y''' - 3y'' + 3y' - y = x2ex, y(0) = 1. y'(0)…

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Q: Find the line integral of F along the parabola y = x² from the origin to (4, 16).

A: Using green's theorem.

Q: Evaluate the iterated integral. x2 3ze dy dx dz Jo

A: triple integration

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: integrate ƒ over the given region.Quadrilateral ƒ(x, y) = x&gt;y over the region in the first…

A: Given,

Q: Find the area enclosed by the closed curve obtained by joining the ends of the spiral r=2θ, 0≤θ≤4.5…

A: Given that  r=2θ, 0≤θ≤4.5 To Find the area enclosed by the closed curve obtained by joiningthe ends…

Q: and y have density flay)=82y tor Find ECX14) and ECYIX) リフズ7679 %3D

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Q: Evaluate the line integral |-ydx + xdy along the curve C : y² = 24x from (24, 24) to (0, 0).

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Q: Evaluate triple integral ſ´, S,2 ¯* dz dx dy .

A: We can solve this as follows:

Q: In whatever way you see fit, evaluate the line integral L(10xy-3y+21x dx+ (15xy=+6xyz*)dy+ (15xy='…

A: given line integral ∫c10xy3z3+3y2z3+21x2z2dx+15x2y2z3+6xyz3dy+15x2y3z2+9xy2z2+14x3zdz   ...i…

Q: The base of a lamp is constructed by revolving a quarter circle  y = (2x-x^2)^0.5  around the…

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Q: Evaluate the double integral. (2x + y) dA, D = {(x, y) | 1 s y s 2, y – 1sx s 1} 328 3.

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Q: Evaluate the line integral $ x*dx + xydx where C is the triangle with vertices at (0, 0), (0, 6) and…

A: Given Line Integral is ∮x4dx+xydy , where C is a triangle with vertices at (0,0), (0,6) and (6,0)…

Q: Compute the surface area of revolution about the x-axis over the interval [0, 1] for y = 4x³. (Use…

A: In this question we have to find the surface area of the revolution about the x-axis.

Q: Use Simpson's Rule e with n=10 Y: X Sin (x), OSXS 27

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Q: Find the area enclosed by the closed curve obtained by joining the ends of the spiral r = 10, 0 < 0…

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Q: Find the defivativesof y o x with resPect Ysxě_eX

A: To find the derivative

Q: Given the curve y=2x^0.5 and line x =y. Find the area bounded and the  distance from the x axis to…

A: Given the curve y=2x^0.5 and line x =y. To find: Find the area bounded and the  distance from the x…

Q: Evaluate the triple iterated integral. 2 2 2 xyz dx dy dz of Jo

A: Given that ∫02∫02∫-12xyz5 dxdydz

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A: The given problem is to evaluate the line integral along the path y=x+2 from points A(0,2) and…

Q: Evaluate the line integral. 7ydx + 6z dy + x dz, r(t) = (2 +t,,1?) for 0 <t<1 (Give an exact answer.…

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Q: Show that 1 y - X 1. Z-y X-Z = 1. %3D alx-y) alz - x)

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Q: 2 Sphere S to be the top half of sphere · x² + y² + 2² SS₁zdS /5 calculate the integral.

A: The given Surface is the top half of the surface x2+y2+z2=a2. To Evaluate: ∬zdS.

Q: g) div(7) for 7(x, y,z) = xyi + yz²j +x²yzk h) curl(ï) for ū(x, y, z) = xzi + xy²j+y²zk

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Q: Evaluate the iterated integral. 2x 2xyz dz dy dx Jx

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Q: let X = * = zrs, find 22u in term f partial deriva bives

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Q: Evaluate the integral ex 2e-2x - 3e2x | Arcsin V6e2x 2 A V3 +C ®Arcsin l V3e2x +C B © 2/2e-2x - 3e2x…

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Q: Calculate line integral F-dr where F(x, y) = (7x + y, 5x + 2y) and C is a rectangle with vertices 0,…

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Q: Evaluate the line integral. L(4x – 8y) ds C:x + y = 100 (4x - 8y) ds = i |

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Q: Evaluate the iterated integral. 3 (2z fIn(x) '3 xe-Y dy dx dz Jo

A: ∫13∫02z∫0ln(x)x e-y dy dx dz

Q: Compute the surface area of revolution about the x-axis over the interval [0,1) for y = 4x'. (Use…

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Q: Calculate the area of the surface defined by r = 5, 0<0<Tl4,0<¢<n/2.

A: Please see the explanation below

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Q: ( b). Je2cos (πx) dx .

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Q: dy ·Use implicit differention find if xcos(2x +3y) = ysinx %3D

A: Given, xcos(2x+3y)=ysinx     Find dydx:

Q: dydx tan x 1. 1+ y²

A: We need to calculate double integral in given order dydx   we use result of inverse Trigonometry…