Double integral question: Evaluating Integrals with Sinusoidal Functions

In summary, the conversation is about evaluating double integrals, specifically one involving sin x^2 and another involving x*sin(x^2). The person asking for help is unsure about which method to use for the first integral and does not understand the notation for the second integral. The helper explains that the first integral does have an x in front of it and provides a step-by-step explanation for finding the values next to the integrand.
  • #1
engineer_dave
35
0
Double integral question...

Homework Statement



Evaluate the integrals shown ( I have attached the file with the integral).

Homework Equations





The Attempt at a Solution



Ok, for the first one, can you tell me how I integrate sin x^2...?? which method should i use? And for the second one, I don't really understand what the R is. What do u have to do to find the values next to to the integrand. Thanks!
 

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  • #2
Can you integrate x*sin(x^2)?
 
  • #3
yea but this doesn't have an x in front of it
 
  • #4
any helpers lol??
 
  • #5
Then I have no idea.
 
  • #6
x is in the limits of the dy integration. Integrating sin(x^2) dy gives y*sin(x^2). Now put in the y limits THEN integrate dx. See, it does have an x in front of it.
 

1. What is a double integral?

A double integral is a mathematical tool used to calculate the area under a two-dimensional surface. It involves integrating a function of two variables over a specific region.

2. How is a double integral different from a single integral?

A single integral calculates the area under a one-dimensional curve, while a double integral calculates the area under a two-dimensional surface. This means that a double integral has two variables of integration, whereas a single integral only has one.

3. What are the applications of double integrals?

Double integrals have various applications in physics, engineering, and other fields of science. They are used to calculate volumes, surface areas, and moments of inertia, among other things.

4. How do I solve a double integral?

To solve a double integral, you first need to determine the limits of integration for both variables. Then, you can evaluate the integral using various integration techniques, such as the substitution method or the double integration by parts method.

5. Can a double integral have a negative value?

Yes, a double integral can have a negative value. This can happen if the function being integrated has negative values in the given region or if the region itself has a negative orientation. In such cases, the negative value indicates that the area under the surface is below the x-y plane.

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