Double Integral bounded by Circle?

In summary, the problem involves a double integral bounded by a circle of radius 2, centered at the origin. To determine the limits for the integrals, one approach is to start with the equation of the circle and solve for y. This will result in two values for y, representing the lowest and highest values that y can take on for a given x.
  • #1
Yezman
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0
Double Integral bounded by Circle?

Double integral of (2x-y)dA bounded by circle of radius 2, centered at origin

I just need to figure out the limits for my integrals... I am basically lost, can someone show me how to break this up. I tried doing what I did with the previous triangle bound one (breaking it into 2) and that didn't work
 
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  • #2


Start with the equation of the circle.
 
  • #3


Are you to do this in Cartesian coordinates? The circle cuts the x-axis at -2 and 2 so x must range from -2 to 2. As SammyS suggested, write the equation of circle. The solve for y. You should get two values for y, corresponding to the lowest and highest values y can take on for a given x.
 

Related to Double Integral bounded by Circle?

What is a double integral bounded by a circle?

A double integral bounded by a circle refers to a mathematical concept where a function is integrated over a two-dimensional region that is bounded by a circle. This involves calculating the area under the function within the circle's boundaries.

What is the formula for calculating a double integral bounded by a circle?

The formula for calculating a double integral bounded by a circle is: ∫∫f(x,y)dA = ∫∫f(r*cosθ, r*sinθ)rdrdθ, where r is the radius of the circle and θ is the angle of rotation.

What is the significance of a double integral bounded by a circle in the field of mathematics?

A double integral bounded by a circle is important in many areas of mathematics, including physics, engineering, and geometry. It allows for the calculation of volumes, areas, and probabilities, and is used in various applications such as calculating electric fields, solving differential equations, and finding the center of mass of an object.

How is a double integral bounded by a circle different from a regular double integral?

A double integral bounded by a circle is different from a regular double integral because the region of integration is restricted to within the boundaries of a circle. This means that the limits of integration and the formula for calculating the integral will differ from a regular double integral.

What are some real-life applications of a double integral bounded by a circle?

A double integral bounded by a circle has many real-life applications, including calculating the area under a curve, finding the volume of a three-dimensional object, and determining the probability of an event occurring within a circular region. It is also used in fields such as signal processing, image analysis, and fluid mechanics.

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