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pb23me
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Homework Statement
Use a double integral to find the area of the region bounded by the curve r= 1+sin(theta)?
Have you done a polar plot?pb23me said:Homework Statement
Use a double integral to find the area of the region bounded by the curve r= 1+sin(theta)?
Homework Equations
The Attempt at a Solution
I can't figure out what theta is integrated from. I've tried from -(pi)/2 -> +(pi)/2 and that doesn't work. I've also tried from 0-> 2(pi) and that doesn't work. I have no clue what I'm supposed to integrate theta to. I would really appreciate some help with this.
Your integral looks good:pb23me said:i put a picture up
Where does the " + 2 " come from ... as inpb23me said:I get (3(pi) + 2)/2
A double integral is a mathematical concept used in calculus to find the area under a two-dimensional curve or surface. It involves integrating a function over a specific region in the x-y plane.
A double integral is used to find the area of a two-dimensional region by breaking it down into smaller and simpler elements, calculating the area of each element, and then adding them together. The smaller the elements, the more accurate the calculation of the area will be.
A single integral is used to find the area under a curve in one dimension, while a double integral is used to find the area under a curve or surface in two dimensions. A double integral involves two integration processes, one for each dimension.
Double integrals are important in science because they are used to calculate the volume, mass, and center of mass of three-dimensional objects. They are also used in many areas of physics, such as calculating the work done by a force or finding the electric field around a charged object.
Yes, double integrals are commonly used to solve real-world problems in fields such as engineering, physics, economics, and even in everyday life. Some examples include calculating the volume of a water tank, finding the mass of an irregularly shaped object, or determining the probability of an event occurring within a certain area.