Suppose f(x, y, z) = phi, and as theta. (a) As an iterated integral, with limits of integration ²+ y² + z² and W is the bottom half of a sphere of radius 3. Enter p as rho, o as B D [[[ s av = ["[³] " f A W dp do do

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Q: 23. Evaluate the iterated integral. f²f (6x²y - a) (6x²y - 2x) dydx ») ff ² (4x² – x²y³²) dydx

A: Definite Integral

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A: Since you have posted more than one question, we solve the first one for you. For the remaining…

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A: Cauchy integral formula

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A: Consider a rectangular box with dimensions x cm , y cm and z cm .…

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Q: 1. Let C be a path along the upper half of a circle from the point P(2,0) to the point Q(-2,0).…

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Q: Write two iterated integrals that equal ∫∫R ƒ(x, y) dA, whereR = {(x, y): -2 ≤ x ≤ 4, 1 ≤ y ≤ 5}.

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A: Consider the provide integral,

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Q: 3 : F = 2yi + 3xj, 6 = ³x³ + 2xy, and h = y — 4x². Let (a) Find each of the following: F-V6 = Vh=…

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Q: 2. Rewrite the integral f(x, y, z)dzdxdy using the order dxdydz.

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Q: Evaluate the integral ² I = (1 + 4y - y²) dy.

A: Recall the formula: ∫1dy=y+C∫yndy=yn+1n+1+C

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Q: When applying the variable change u-cosy in the in the following integral: [ f(cos y) sen³y dy What…

A: The given integral is: I=∫fcosysin3ydy   ...1

Q: 1) Evaluate the following iterated integrals. › S₁ S² b) x-y (x+y)3dydx (x+y)3dxdy So So

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Q: 7. Use the Fundamental Theorem of Line Integrals to evaluate S(6xy, 3x² + 6y²) · dr where C is any…

A: Line integral theorem

Q: 2 Evaluate the following contour integral ez $21-3 |2|=3 2(2-2) 3dz,

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Q: a) by parametrizing C, b) by using the Fundamental Theorem of Line Integrals.

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Q: 1. Evaluate the integral If. (430 R (4x + 16y)dA, where R is the parallelogram bounded by the lines…

A: To find the given integral , we can change the given integral in  terms of 'u' and 'v' .

Q: .2 Evaluate the line integral xy dx + x-dy, where C is the path going counterclockwise around the…

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Q: By applying the convolution theorem to calculate L-1(14/[(s + 4)² + 25] ), an adecuate integral for…

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