aaronfue said:Homework Statement
∫∫ (2x+4y+1) dA, R: y = x[itex]^{2}[/itex], y = x[itex]^{3}[/itex]
Homework Equations
∫R∫ f(x,y) dA
The Attempt at a Solution
Since there was no direct question, I assumed to just evaluate with whatever I was given.
I would really like to make sure that my integrals are set up correctly:
[itex]∫^{1}_{0}[/itex] [itex]∫^{x^{2}}_{x^{3}}[/itex] (2x+4y+1) dydx
Double integration over a region is a mathematical concept in which a function is integrated twice over a two-dimensional region. It involves calculating the area under a curve in two directions.
The purpose of double integration over a region is to determine the volume under a surface of a three-dimensional object. It is also used to calculate the mass, center of mass, and other physical properties of an object.
The first step is to set up the limits of integration for each variable. Then, the function is integrated with respect to one variable, and the result is integrated with respect to the other variable. The final step is to evaluate the double integral using the limits of integration.
The two main methods for evaluating double integration over a region are the iterated integral method and the polar coordinates method. The iterated integral method involves evaluating the integral in two stages using the limits of integration. The polar coordinates method is used when the region is best described using polar coordinates.
Double integration over a region has various applications in physics, engineering, and economics. It is used to calculate the moment of inertia of a three-dimensional object, the surface area of a curved surface, and the average value of a function over a region. It is also used in calculating the work done by a force and in determining the volume of irregularly shaped objects.