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stanford1463
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How do you solve the double integral of xe^(xy)? bounded by x=0, y=1, x^2-y=0. I used both x-simple and y-simple methods but neither worked..I don't know what the limits are...thanks!
jeffreydk said:Yea that integral is messy. I tried to get a numerical integration of the entire double integral you wanted and it's complex; I get
[tex]\int_0^1\int_{x^2}^1xe^{xy} dy dx = 0.376377+ (3.9255\times 10^{-16})\imath[/tex]
A double integral is a mathematical operation that calculates the area under a curve in a two-dimensional space. It is represented by the symbol ∫∫ and is used to find the volume, mass, and other physical quantities in physics and engineering.
The double integral of xe^xy is often used to find the expected value of a function in probability and statistics. It is also used in economics and finance to calculate the expected return on an investment.
The double integral of xe^xy can be solved by first evaluating the inner integral with respect to one variable, and then integrating the result with respect to the other variable. This can be done using techniques such as integration by parts or substitution.
The double integral of xe^xy is equivalent to taking the single integral of e^x with respect to y, and then integrating the resulting expression with respect to x. This shows the connection between the two operations and how they can be used to solve different types of problems.
The double integral of xe^xy has various applications in physics, engineering, and economics. For example, it can be used to calculate the center of mass of a two-dimensional object, the volume of a solid of revolution, or the expected value of a financial asset. It is also used in fields like image processing, where it can be used to find the average color intensity of an image.