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To find the region inside the cardioid r = 1+ cos(θ) and outside the circle r = 3cos(θ), we first find their points of intersection and then calculate the areas of both shapes using integrals Set up the double integral as efficiently as possible, in polar coordinates, that is used to find the area inside the cardioid r= 1 + cos o until it intersects with r= 1 + sin 8. The final area is determined by subtracting the area of the circle from the area of the cardioid.

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Use double integral in polar coordinates to find area of region that is inside the cardioid r = 1 + cos (t) and outside the circle r = 3cos (t).more Use a double integral to find the area of the region inside both the cardioid r= 1 + sin 0 and the cardioid r= 1 + cos o To find the area, we use a double integral in polar coordinates

The radial coordinate r will vary from the circle to the cardioid, i.e., from r = 3 cos θ to r = 1 + cos θ, and θ will vary from π 3 to π 3.

This question aims to find the area of the region described by the given equations in polar form The discussion focuses on calculating the area inside the cardioid defined by r = 1 + cos (θ) and outside the circle defined by r = 3cos (θ) using double integrals The intersection point of the two curves is found at θ = π/3, leading to the identification of two distinct regions for integration. Use a double integral to find the area of the region

The region inside the cardioid r=1+costheta and outside the circle r=3 costheta. To find the area of the region inside the cardioid r = 1 + cos(θ) and outside the circle r = 3cos(θ), we will use a double integral in polar coordinates The region of interest can be identified by determining the intersection points of these two curves. Ask question asked 11 years ago modified 9 years, 8 months ago