(b) Then, evaluate ln etty dA by using polar coordinates where R is the region in (a).

Q: Find the area of the region Inside the cardioid r = a(1 + cos u), a > 0

A: Given  r=a1+cosu, a>0

Q: Use a polar double integral to find the area enclosed by the threepetaled rose r = sin 3θ.

A: The equation of the petal is given as r = sin 3θ.First, we will sketch the region. If we can find…

Q: ) Evaluate the integral dy dx using polar coordinate

A:

Q: Find the area of the surface obtained by rotating the given curve about the x-axis. - 10 10 cos (0),…

A: Find the derivatives with respect to θ

Q: Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral. 4…

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Q: # 3. Sketch the region R inside the curve r = 1+ cos 0 and outside the circle r = 1 and use polar…

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Q: Use the integration capabilities of a graphing utility to approximate the area of the region bounded…

A:

Q: change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral.

A:

Q: Evaluate the iterated integral by converting to polar coordinates V81 – x2 e-x2 - y dy dx

A: see 2nd step

Q: A6] Evaluate the integral J: J over the area of a circle of radius 2, using polar coordinates.

A: We have, J=∫∫Ax2y2dxdy   Equation of circle is, x2+y2=22   In polar coordinates, x=rcosθy=rsinθ Here…

Q: Ex4: Find the centroid of the region that lies inside the cardioids r = a(1+ cos8) and outside the…

A:

Q: change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral.

A: Given:   (i) To change the Cartesian integral in to polar integral. (ii) To evaluate the polar…

Q: Consider the polar curve C1 given by r = sin(0), for 0 € [0, 27), Find the area of the region under…

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

Q: Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral. 9…

A:

Q: 3. Find the area using the double integration in polar coordinates 23 4 r=2+ sin 0 ++NIa

A: Consider the provided figure,

Q: 1 Use polar coordinates to evaluate the area of the region bounded above by the circle x2 + y² - 2y…

A: Given circle is x2+y2−2y=0 and y=12. We have to find the area of the region bounded above by the…

Q: Find the area inside the curve r 12 = sin 20. %3D

A:

Q: 4. Q1. Using Polar coordinates, find the area of the region R as shown in figure R

A: Using polar coordinates the area is given  by:  A=∬Rrdrdθ…

Q: b. Sketch the area over which the double integral -dydx is taken, √a²-x²-y² where a > 0. By changing…

A: We have given that y=a2-x2which is a semicircle at origin with radius  a.and…

Q: Find the area enclosed by the curve r = 3sin 2θ defined in polar coordinates.

A: Given curve r=3sin2theta Solving  the equation  as shown below

Q: Find the surface area of the object obtained by rotating y = sin(2x) , 0<x< about the x-axis.

A:

Q: L **y dx dy -Va2-y2

A: Given ∫0a∫-a2-y20 x2ydxdy

Q: Determine the y-coordinate of the centroid of the area under the sine curve shown. y Answer:y- Mi…

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Q: Vi-y sin (x2 + y2) dx dy

A:

Q: change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral.

A: We have to change the Cartesian integral into an equivalent polar integral. Then evaluate the polar…

Q: Evaluate the iterated integral by converting to polar coordinates. 9. 6x - x2 ху dy dx

A:

Q: 2. Find the common area enclosed by the polar curves. r= 3cose r= 1+cose

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Q: b) Use the polar coordinate to find the integral S+y) dxdy

A: See the attachment

Q: Find the area of the region enclosed by the inner loop of the curve. r = 6 + 12 sin(0)

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Q: Evaluate the integral by converting to polar coordinates. 2. V4-x2 cos(x + y) dy dx

A: To evaluate the given integral by transforming it into polar coordinates.

Q: r 2e-20

A:

Q: 2. Use the disk method to find the volume of the solid obtained by rotating the shaded region about…

A: We will solve the problem

Q: Given two polar curves and r=2cos2θ , r =1 as in Figure 1. Find the area of the shaded region by…

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Q: Caluelate the integral using polar coordinates dA ,

A:

Q: Sketch the region and find its area. - The region between y = sin z and y = sin 2r, for 0< I<T.

A: Given: The regions y=sin x and y=sin 2x Consider the two curves are equal, sin x =sin 2x  sin 2x -…

Q: 2 v2x-x2 xydydx 0 0

A:

Q: Determine the y-coordinate of the centroid of the area under the sine curve shown. y = 3 sin 11 3…

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Q: find the mside the r= 2a cos curve of region area the outside the r=Q arcle .

A: From given,we have to find the area of the region inside r=2a cos(theta) and outside r=a

Q: Use a polar double integral to find the area enclosed by the multi-petaled rose r = cos 4θ.

A: Consider the given polar curve r=cos4θ Draw the given polar curves.    The polar curve has 8…

Q: a (0 32. x²y dx dy -Va?-y?

A: Given Integral, I=∫0a∫-a2-y20 x2y dx dy Use Polar coordinates,  x=rcosθ, y=rsinθ, dxdy=rdrdθ limits:…

Q: 2-y² (x+ y) dx dy

A: Given, the integral                           We have to calculate this integral by converting it…

Q: find the area of the surface formed by revolving the cardioid r= a(1+cosθ) about the x-axis

A:

Q: Q;: A- Use Simpson's Rule with n=2 subintervals, evaluate the integral -L Inx.dx , and compare the…

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Q: Find the exact area between a large loop and the enclosed small loop of the curve r = 1 + 2 cos(30).…

A: (1).    The given curve is: r=1+2cos3θ

Q: Evaluate the integral by changing to polar coordinates: ff, sin(x² + y²) dA, where Ris the region in…

A:

Q: Evaluate the given integral by changing to polar coordinates. ∫∫R sin(x2 + y2) dA, where R is the…

A: The integral is ∫∫R sin(x2+y2) dA The polar coordinates are x=r cos θy=r sin θ dA=r dr dθ…

Q: Find the area enclosed by the polar curve r = 4e0.70 on the interval 0 <0< and the straight line…

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Q: Evaluate the integral: L x2 + y² dy dx by using polar coordinates.

A: