2. Evaluate Vr2 + y? dy dx by switching to polar coordinates.

Q: /25– x² 1. Evaluate (x2 + y? )3 dy dx by converting to polar coordinates.

A: Evaluate the double integral by using the charge of polar coordinates

Q: 2. Compute dy dx (x² + y²)' by first changing it to polar coordinates.

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Q: 4–x2 Sở SY dy dx using polar Evaluate 2x-x2 Coordinates.

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Q: 2² dz dx dy By converting to spherical coordinates, evaluate

A: Given:  ∫02∫04-y2∫x2+y28-x2-y2z2dzdxdy we need to find following integeral by using spherical…

Q: By using polar coordinate method, solve the double integral: 1-x x² + y? dy dx

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Q: Q3//A:- Verify that dV = p² sin p dp d0 do when using spherical coordinates.

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

Q: For the parametric equations: = 26e4 and y = 46et dx () dt %3D dy (ii) dt dy (ii) %3D dx

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Q: 8-a2-y By converting to spherical coordinates, evaluate 2² dz dx dy

A: Let us consider the rectangular coordinates (x,y,z) then the relation between spherical coordinate…

Q: Express y=x^2 in polar coordinates.

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Q: For the parametric equations: = 48e2 and y = 4le %3D %3D da (*) dt dt dy (6) da %3D

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Q: Integrate by changing to polar coordinates. (4 - x2 tan V 4 -1(Y) dy dx

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Q: 1 (x+y')* dy dx -J3X 2

A: Double integration of function gives the area under the function curve. Double integration can be…

Q: 4. Integrate L e-° dxdy by converting to polar coordinates, and ase that result to integrate J e dx.

A: This problem is convert to pollar form and then solve so,......

Q: %3D For the following polar equation, compute dy/dx when 0 = 1/2, r = 3 + 2cos 0

A: Recall:          If we have x= r cosθ and y=r sinθ .and given a curve r=f(θ), then we can write as…

Q: 6. By converting to spherical coordinates, evaluate 22 dz dx dy. 0.

A: triple integral

Q: In changing variables to polar coordinates, the dA in f(x, y) dA becomes „2 dr de. True False

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Q: Convert to polar equation. Express rinterms of Q 4x + y = 5

A: The objective is to convert in terms of polar equation.

Q: For the parametric equations: = 48e2 and y = 41et da (*) dt (6) dt %D dy (s) da %3D

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Q: 3. Express the equation y = mx + b, where m and b are constants, in plane polar coordinate.

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Replace the Cartesian equation x² + y² equation. OA) r sin² 0 = 4 cos 0 B) r = 4 sin 0 Oc) r = 4 cos…

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Q: er the polar curve r=O, dy at 0 = %3D dx

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Q: Verify that dV = p sin o dp de dy when using spherical coordinates. %3D

A: We have to represent a differential element.

Q: Match the given parametric equations with one of the parametric curves. x-3- sint, y = 5+ cost O A.

A: To sketch the given parametric equation :- x = 3 -sin t  and  y = 5+cos t

Q: 25-r2 Evaluate (x2 + y?)3 dy dx by converting to polar coordinates.

A: we have to evaluate the following

Q: 2. \ Evaluate •V4-2² dydx + dydx 2x-r2 using polar coordinates.

A: We have to evaluate the integral using polar coordinates.

Q: Find e-a* -y" dx dy using polar coordinates.

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Q: Use polar coordinate to evaluate (x² + y* )² dx dy . Leave your answer correct to two decimal…

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Q: Use polar coordinates to evaluate 2/2 dydx. 3 1 0, (x²+y?)? O 5 Оз 6 O 2 O 1 O 4

A: To determine: The value of the integral  using polar coordinates, ∫12∫0x22x2+y232dydx.

Q: TY 7. Compute dy dx by converting to polar coordinates. V4-2 x2 + y2

A: 7. Given integral is ∫02∫-4-x20xyx2+y2dydx The objective is to solve the integral using polar…

Q: 7) Evaluate IT !! (x + y)dxdy y by switching to polar coordinates.

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Q: Verify that dV = p² sin y dp de dp when using spherical coordinates. %3D

A: You have posted multiple questions. As per the instruction, we will be answering only the first…

Q: consider the following set of parametric equations: x = 6tanhθ ; y = 3sechθ Calculate d^2y/dx^2

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Q: Find the dy/dx of the parametric equations given: x= 2t² – t and y= t³ – 2t – 1

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Q: l+vI+r² xy dydx -z 1-VT-

A: ∫01∫1-1-x21+1+x2xydydxTo transform to polar coordinates and calculate

Q: Convert to Polar coordinates. (r 20 & 0 < 0 < 2n) (x, y) = ( -1, v3 )

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Q: Eliminate the parameter t from the parametric equation x = 3 sint y = 3 cost 0 ≤t≤ 2π.

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Q: Sketch in Polar X =-Jy %D

A: This can be done by the equations for cartesian to polar conversion which is derived in step 2.

Q: aluate the dnd to polar

A: Given that, ∫0a∫02a-x2xx2+y2dxdy Take x=rcosθ, y=rsinθ where 0≤θ≤2π.

Q: x = 4 cos t and y = 4 sin t 0sts 4

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Q: Use polar coordinate to evaluate (x² + y² ) dx dy - Leave your answer correct to two decimal places.

A: To evaluate: ∫01∫01-y2x2+y2dx dy

Q: d) Find the slope of the parametric equations x=2+3sin and y=0-cose at 0=

A: Given: x=2+3cosθ and y=θ-cosθ   As we know that; The slope of the tangent line to the given curve is…

Q: 3) Use polar coordinate to evaluate S'S_√x² + y² dxdy.

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Q: QJchange to Polar ( dxdy - Ji-y?

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Q: Evaluate /1-(y-1)² by first changing it to polar coordinates. 219 dx dy

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Q: 3. Change (r+1)²+y² = 1 to an equiv- alent polar equation

A: GIVEN (x+1)2+y2=1

Q: What is the slope of the line tangent to the polar curve r 202 when 0 = T? A 4 7/2 C 2/T - 27?

A: r=2(theta)^2 theta=pi To find: slope=??

Q: 2 Evaluate V4-x? Jo J2- dy dx using polar V 2x-x2 Coordinates.

A: Solution:-

Q: Change to polar integral 1 -(2²+y?) dydx e 0 -/1-2?

A:

Q: 3 V9-y2 / / (x² + y²) dx dy

A: