Double Integral Help: |cos(x+y)| over [0,pi]x[0,pi]

In summary, the conversation suggests using methods such as splitting up the region of integration and using polar coordinates to solve the double integral of |cos(x+y)| over the rectangle [0, pi]x[0,pi]. However, using polar coordinates is not recommended and it is advised to cut the square along the lines x+y=pi/2 and x+y=(3*pi/2) to properly integrate the function.
  • #1
eckiller
44
0
doubleIntegral( |cos(x+y)| dx dy ) over the rectangle [0, pi]x[0,pi]

I tried several ways to split the integral up so that I could remove the absolute value sign and integrate. However, I did not get the correct answer, so I must be splitting it wrong. Can someone show me how to split the region of integration up so I can integrate iteratively?
 
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  • #2
At a glance, not saying this will work, but try using polar coordinates? ie x^2+Y^2=r^2 and so on.
 
  • #3
FunkyDwarf said:
At a glance, not saying this will work, but try using polar coordinates? ie x^2+Y^2=r^2 and so on.

Polar coordinates are a bad idea. Cut the square along the lines x+y=pi/2 and x+y=(3*pi/2) - since this is where the cos changes sign.
 

Related to Double Integral Help: |cos(x+y)| over [0,pi]x[0,pi]

1. What is a double integral?

A double integral is a type of mathematical calculation used to find the volume under a three-dimensional surface, or the area of a two-dimensional region, by integrating over two variables.

2. How do you solve a double integral?

To solve a double integral, you need to first determine the limits of integration for both variables. Then, you can use the properties of integrals, such as linearity and the fundamental theorem of calculus, to evaluate the integral. In this particular case, you would need to use techniques like substitution or integration by parts to simplify the integrand and then evaluate the integral.

3. What is the meaning of the limits of integration in a double integral?

The limits of integration in a double integral represent the range of values that the two variables can take on. In this problem, the limits of integration are [0, pi] for both x and y, meaning that the integral is being evaluated over the square region with corners at (0, 0) and (pi, pi).

4. Why is the absolute value of cos(x+y) used in this double integral?

The absolute value of cos(x+y) is used in this double integral because it ensures that the function being integrated is always positive. Without taking the absolute value, the integral would evaluate to zero since cos(x+y) has both positive and negative values over the given region.

5. What is the significance of the symbol "dx dy" in a double integral?

The symbol "dx dy" in a double integral represents the order of integration. Since this is a double integral, it means that the integral is being evaluated with respect to x first, and then with respect to y. This is important to note because changing the order of integration can result in a different value for the integral.

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