Finding area using double integral

In summary, a double integral is a mathematical concept used to find the area under a curved surface in two dimensions. It differs from a single integral in that it finds the area under a surface rather than a curve, and is often represented as two single integrals. The process for finding the area using double integral involves setting up the integral and evaluating it using integration rules. Its applications include calculating mass, volume, and revenue, but it has limitations in that it can only be used in two dimensions and may have difficulty with complex boundaries.
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Lorenc
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Hey guys, how are you? I was studying for my calculus final and stumbled upon a peculiar function. Now I have to find the area bounded by the function (x^2+y^2)^3=xy^4 using a double integral. Now, the problem is that the graph is totally unknown to me (I have some ideas but I am not shure). A substitution with u and v, doesn't seem to work and going to polar doesn't work either :/ Maybe I am doing something wrong, I don't know. Can anybody help me? Thank you in advance :)
 
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please repost using the template
 

What is a double integral?

A double integral is a mathematical concept used to find the area under a curved surface in two dimensions. It involves taking the integral of a function over a specific region in the x-y plane.

How is double integral different from single integral?

A single integral finds the area under a curve in one dimension, while a double integral finds the area under a surface in two dimensions. Double integrals are often represented as two single integrals, with one representing the area in the x-direction and the other in the y-direction.

What is the process for finding the area using double integral?

The process for finding the area using double integral involves setting up the integral with the appropriate limits and then evaluating it using integration rules. This involves calculating the area of small rectangles within the region and then summing them up to find the total area.

What are the applications of double integrals?

Double integrals have many applications in mathematics and science. They are commonly used in physics to calculate the mass, center of mass, and moment of inertia of an object. They are also used in engineering to calculate the volume of a solid, and in economics to calculate total revenue and profit.

What are the limitations of using double integrals to find area?

Double integrals can only be used to find the area of a region in two dimensions. They cannot be used to find the volume of a solid in three dimensions. Additionally, some regions may have complex boundaries that make it difficult to set up the integral and accurately calculate the area.

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