Express the double integral (1+x)dA, where R is the region in the upper half-plarie (i.e. y 2 0) between (1+. R the circles x2+ y2 = 9 and x2+y = 16, in polar coordinates. %3D 16 I Pcose +r) dr de | (rcose+1) dr de (rcose +1) dr de 3. 16 I Pcose+r) dr de 6. Pcose+r) dr de TT I Pcose +r) dr de 3

Q: 5. Let D be the planar region that is inside both polar curves r = 1+ cose and r = 1+ sine, but is…

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Q: Evaluate √√x² + y2 dA, where D is the domain in the figure and a = 26. 26 12/6 1/₁₂ √ x² + y² α ^ =…

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Q: Sketch the region R in the first quadrant between the circles (x – })° + y² = } and (r -)? + y? = .…

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Q: (b) Compute using polar coordinates quadrant common between circle x² + y² = 2x and circle x² + y² =…

A: Given circle is, x2+y2=2x and x2+y2=1 Evaluate ∬s ca y dA such that s is the area of the region in…

Q: et R={(x,y)=R² | x² + y² ≤4y}. Draw it. Write it in polar coordinates.

A: R=x, y∈ℝ2|x2+y2≤4y

Q: 3) Evaluate the iterated integral by converting the to polar coordinates -√₂x-x² a) √²ty² dydx…

A: Given that, The integrated integral: (a) ∫02∫02x-x2x2+y2dydx,  such that , the region is…

Q: A region R is enclosed by the cardioid r =1+ cos 0 in the secone quadrant. i) Sketch and shade the…

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Q: 3. a) Find polar coordinates (r, 0) of the point (1, -/3), where r> 0 and 0 <0 < 2 p2 = x² + y?, tan…

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Q: Let u = u(x, y), and let (r, 0) be polar coordinates. Verify the re- lation |V? = u; + zuổ Hint:…

A: Let u = u(x, y) and let (r, θ) be polar coordinates.

Q: Could you explain why r goes form 0 to 7cos theta please

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Q: Q5: Find the area of region enclosed by the polar function r = 4 – 4 sin 0

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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: Find plane area inside polar function r 2 and outside polar function r= -2sint in thisd quurter.

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Q: Identify the correct plot that describes the polar region R-{(r, e )| 2 srs 5, n/2 s 0 s 3n/2}. -3-2…

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Q: 3 Evaluate the integral cos(x² + y²)dydx by converting to polar coordinates 0 0

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Q: 5. Find two sets of polar coordinates for the Cartesian point (-7, 7/3) such that 0<0<2T.

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Q: Evaluate fS (3x + 4y²)dA by changing it into polar coordinates over the region in upper half plane…

A: In polar coordinates

Q: Convert S ² (3 cos 0 + 4r sin² 0) drde СТ [² S²³ (3x+4y2) dyda into polar coordinates 3r+4r sin 0…

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Q: Which of the following is equivalent to the following integral when converted to polar coordinates?…

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Q: Let w = f(x, y) and x, y in polar cordainate then (fr)² + (fy)² =

A: We are given that w=f(x,y)            ........(1) x, y are in polar coordinates. So, in polar…

Q: 6 Evaluate (3x+4yʻ) dA by changing to polar coordinates, where R is the region in the upper…

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Q: * For z = 4 + 4 i, find z^ 4 in polar form z^4 = (V32 )^4 e^(i T/4) O z^4 = (32 )^2 (cos n +i sin n)…

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Q: solve the differenctil equation by undtermeind coefficients y'' +2y = -18x2e2x   y(x) = ?

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Q: Q5/ Consider the following polar curves r = 2 - 2cos0 and r 5+2cose 1. Graph the above equations in…

A: For the range 0≤θ≤2π, construct a table of values for both curves followed by graphs of each, as…

Q: Question 10 Evaluate the double integral ff (2x + 5y) dA by changing to polar coordinates where R is…

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Q: Find the area of the region inside the polar curve r=5 +cos 8 that is lying in the second quadrant.

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Q: Evaluate ∫ ∫ √ (x2+ y2) dA where R is the portion of the annulus 1 ≤ x2 + y2 ≤ 16 with y ≤ 0 using…

A: We have to evaluate the double integral.