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nysnacc
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Homework Statement
Homework Equations
Average (area) = 1/Area * integrate of polar
The Attempt at a Solution
y= r* sin theta
x= r* cos theta
r^2 = x^2+y^2
x^2 + y^2 =r^2... OH, so only r not root r! and other than that, its fine?BvU said:Why the square root ?
And I got the answer as ⅓ aSsnow said:now it is ok,
A polar coordinate integral is a type of integral used to find the area under a curve in polar coordinates. It is similar to a regular integral, but the function is expressed in terms of polar coordinates (radius and angle) instead of Cartesian coordinates (x and y).
The main difference is that a polar coordinate integral uses polar coordinates, while a regular integral uses Cartesian coordinates. This means that the limits of integration and the function being integrated will be expressed in terms of radius and angle instead of x and y.
The formula for a polar coordinate integral is ∫r²dθ, where r is the radius and θ is the angle of the polar function being integrated. This formula is used to find the area under a curve in polar coordinates.
Polar coordinate integrals are commonly used in physics and engineering, particularly in problems involving circular or rotational motion. They are also used in calculating the area of regions bounded by curves in polar coordinates.
Some common applications of polar coordinate integrals include calculating the moment of inertia of an object, finding the center of mass of a region, and calculating the work done by a force in circular motion.