Double integral, change order of integration, int(0,1)int(y,1)(e^(-x^2)*y^2)dxdy

In summary, the conversation is about someone having difficulty solving a problem and needing help with changing the order of integration. They also mention that they have an answer and provide the integration equation. They thank the person in advance for their help.
  • #1
acapa
2
0
hey,

i'm having some difficulties solving a problem. i want to know exactly how to go about solving it, since i am studying for a final exam. i know that i need to change the order of integration, but i'd also like to see how it's done correctly, since no official answers are provided... (my answer, btw, is (1-2/e)/6)

int(0,1)int(y,1)(e^(-x^2)*y^2)dxdy

where int(lower limit, upper limit)

thanks so much in advance!
 
Last edited:
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  • #2
Changing the order of integration is easy, but I don't see how it helps.

If you want to do y first, then you have (0,1) for x and (0,x) for y.
 
  • #3
thank you so much!
 

1. What is a double integral?

A double integral is a type of mathematical operation used to calculate the volume under a surface in two-dimensional space. It involves integrating a function over a region in the xy-plane.

2. How do I change the order of integration in a double integral?

To change the order of integration in a double integral, you can use the concept of Fubini's Theorem. This theorem states that if the function being integrated is continuous, then the order of integration can be changed without affecting the value of the integral.

3. What does the notation "int(0,1)int(y,1)(e^(-x^2)*y^2)dxdy" mean?

This notation represents a double integral, where the limits of integration for the inner integral are y and 1, and the limits of integration for the outer integral are 0 and 1. The function being integrated is e^(-x^2)*y^2.

4. What is the significance of the function e^(-x^2) in the given double integral?

The function e^(-x^2) is known as the Gaussian function and it represents a bell-shaped curve. It is commonly used in statistics and probability to model random events. In the given double integral, it is being multiplied by y^2, which can represent the height of the surface being integrated over.

5. How can double integrals be applied in real-life situations?

Double integrals have many applications in science and engineering, such as calculating the volume of a three-dimensional object, finding the center of mass of a two-dimensional object, and determining the total charge or mass of a region with varying density. They can also be used in economics to calculate the total revenue or cost of a product with varying prices.

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