Calculate the total length of the circle r = 9 sin(0) as an integral in polar coordinates.

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: Use the integration capabilities of a graphing utility to approximate the area of the surface formed…

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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: Find the area of the region that lies inside both polar curves r = 2 and r = 4 cos 0.

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Q: What is the area of the area outside the polar curve r= 1+ cosoc and inside thepolar curve r-3 cos o…

A: We will solve the problem

Q: Evaluate the integral by converting to polar coordinates. cos(r² + y²) dy dx = 0.

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

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

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Q: Change the Cartesian integral to an equivalent polar integral and then evaluate: 225-y² (x² + y²) dx…

A: ∫015∫0225-y2x2+y2dxdy=50625π8

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

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Q: Find the area of the region in the plane enclosed by the cardiod : r=2(1+cos(theta)) where theta…

A: The area enclosed by the cardioid is

Q: State the formula for the Area of the sector bounded by a polar curve r = f (θ ) and two rays θ = α…

A: Given: The equation of polar curve is: r=fθ where, α≤θ≤β

Q: I have been getting 18pi as the answer but that is incorrect please help

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

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Use polar coordinates to find the integral 16 - x² - y? dx dy where R is the circle x? + y? < 4.

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Q: Calculate the total length of the circle r = 4 sin θ as an integral in polar coordinates.

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Q: Evaluate the double integral / z² + y°dA, where Dis the disc with center the origin and radius 2, by…

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Q: Use the parametric equations of an ellipse x = acos(theta), y = bsin(theta) on the interval[0,2pi]…

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Q: Convert the integral to polar coordinates and evaluate. 4 – y2 (x2 + y2)2 dx dy -V4 - y2

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Q: Evaluate the double integral // (3x – y) dA, where R is the region in R the first quadrant enclosed…

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Q: Find the area of the surface generated by revolving the parametric curve x = cos² t, y = sin² t (0 ≤…

A: To find: The area of the surface generated by revolving the curve about y-axis. Given: The…

Q: xez²+y? dy dx

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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: Consider the polar curve given by r=40' where 0<0<r. Set up, but do not evaluate, an integral which…

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Q: Use the parametric equations of an ellipse x = 10 cos 0 y = 22 sin 0 0 ≤ 0≤2T to find the area that…

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Q: Determine the area under the parametric curve given by x = 2(0 sin 0), y = 2(1 - cos 0), 0≤ 0 ≤ 2π.

A: I have given the answer in the next step. Hope you understand that

Q: Use polar coordinates to integrate under z=xy above the first quadrant of the unit circle on the xy…

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Q: Caluelate the integral using polar coordinates dA ,

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Q: 4. y = sin2r, 0 sa Find the area of the surface of rotation obtained by rotating the curved segment…

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Q: Explain why the element of area in Cartesian coordinates dx dybecomes r dr dθ in polar coordinates.

A: the integral which is used to find the area in cartesian coordinates is  ∫Df(x,y)dxdy…

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

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Q: 2 v2x-x2 xydydx 0 0

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Q: Find the double integral SSR V10-2²-y² dA by changing it to polar coordinates, where R is the region…

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Q: Calculate the area bounded by the circler = 2 and the rays 0 = 1t and e = n as an integral in polar…

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Q: ) Evaluate the double integral /| (2x – y) dA, where R is the region in the first R quadrant…

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Q: Compute the surface area of the surface generated by revolving one arch of the cycloid c(t) = (10t –…

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Q: Describe in polar coordinates the region in the first quadrant between the circles of radius 1 and…

A: The Polar equation of a circle of radius 1 and having center at the origin is: r = 1

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

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

A: Given,          ∫-aa∫-a2-x2a2-x2dydx

Q: 'Evaluate the double integral (3x – y) dA, where R is the region in the first quadrant enclosed by…

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Q: Find the area of the plane z = 4x + y for all (x, y) = R where Ris the region in the first quadrant…

A: Consider the equation of the plane, z=4x+y for all x,y∈R,where R is the region in first quadrant…

Q: Find the area of the surface obtained by rotating the curve of parametric equations T = 2 cos 0, y =…

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Q: Evaluate the double integral // (2x – y) dA, where R is the R region in the first quadrant enclosed…

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Q: Evaluate the double integral x² + y*dA, where D is the disc with center the origin and radius 4, by…

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Q: b) Sketch the graph and find the points on the cardioid r=a(1+cos) at which tangent lines are…

A: Consider the equation of the cardioid, r=a1+cosθ The graph will be,

Q: Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral. 3…

A: we have to find integral value

Q: 2-Change the Cartesian integral in to an equivalent polar integral, then evaluate polar integral (x²…

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Q: Find the area inside the cardioid with a polar curve of r=4+4cos(θ).

A: Find the area of inside the cardioid with a polar curve: