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

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: Use polar coordinates to evaluate (x² + y° )% dy dr.

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Q: 4y-y² y(x² + y²)² -dxdy o Jy *use polar coordinates

A: The given integral is: I=∫02∫y4y-y2 yx2+y22x5 dx dy

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: Find in the parametric equation d'y dx² x = 5 sin² t y = 2 cost 0≤t≤ 2π.

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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: 3. Evaluate/calculate using polar coordinates. -1/2 cV1-x² А. M-X" xy/x2 + y² dydx ху,

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Q: 2. Compute [²√x by first changing it to polar coordinates. 1 -√3x (x² + y²) ² 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: Replace the Cartesian equation with an equivalent polar equation. x² + y² - 4x=0 O A. r cos²0=4 sin…

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

A: We have to represent a differential element.

Q: V16-x dy dx . +y Use polar coordinate to evaluate Leave your answer correct to two decimal places.

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Q: Integrate by changing to polar coordinates. '3 8x dx dy

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Q: 2) Use polar coordinate dydx (1+ x² + y° )'?

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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: What is the formula for the derivative for dy/dx for a polar curve r=f(theta)?

A: Given that

Q: Q 4/ Use polar coordinate to evaluate 1v1- x2 + y? dydx

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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: 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: Pपा+ with a focus at co,-1) 'and directrix y=l

A: Vertex will be the midpoint of y=1 and (0,-1)  That is (0,0) So, (h,k)=(0,0)

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: 1.5 3-X Evaluate the integral *dy dx using polar coordinate

A: Follow the procedure given below.

Q: Q5) Evaluating in polar coordinates: *+ y*)dydx

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Q: Find the area between 0 = 0 and 0 = π/2 of the polar curve r = 1 + sin 0

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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: 2y )dx - (x +3 cos y)dy around the parallelogram havi - 6

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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: Convert the polar equation to a rectangular equation. r= 6 cos e + 5 sin 0 О х2 - у2 - 6х + 5y O x²…

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Q: V8-x2 Use polar coordinates to evaluate 6 I dy dx. x2+y2+5

A: To evaluate the given integral by using polar coordinates

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

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

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Q: 2y-y y dx dy a. Using Polar coordinates Evaluate

A: As you didn't mention the question numberto be solved so i solved First 2 question.For remaining…

Q: Find the area of the region. Interior of r = 4 + 3 sin 0 (below the polar axis)

A: Given that         r = 4 + 3 sin (theta) Here we have to find the area of the region below the polar…

Q: Q3/|A:- Verify that dV = p² sin o dp do dp when using spherical coordinates. %3D

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

A: Solution:-

Q: Change the spherical equation below into cylindrical coordinates! tan2(Φ) = 1

A: Any point in the cylindrical coordinate system is represented as r,θ,z . Any point in the spherical…