- #1
abubakar_mcs
- 2
- 0
Hi! Need help in solving this double integral:
1 1
∫ ∫ |x-y| dydx
0 0
Thanks in anticipation.
Regards,
Aby.
1 1
∫ ∫ |x-y| dydx
0 0
Thanks in anticipation.
Regards,
Aby.
abubakar_mcs said:Hi! Need help in solving this double integral:
1 1
∫ ∫ |x-y| dydx
0 0Thanks in anticipation.
Regards,
Aby.
mathman said:Change |x-y| to x-y for y < x. Change |x-y| to y-x for y > x.
You now have two double integrals which you can do easily (y integral inner for both).
A double integral is a type of integration that involves finding the area under a 3-dimensional surface. It is typically used to solve problems involving volume, mass, and other physical quantities.
To solve a double integral, you need to first determine the limits of integration for both the inner and outer integrals. Then, you can use either the rectangular or polar coordinate system to set up the integrals. Finally, you can evaluate the integrals using various techniques such as substitution or integration by parts.
An absolute value function is a mathematical function that returns the distance of a number from 0 on a number line. It is represented by two vertical bars surrounding the input, and it always results in a positive output.
In a double integral, the absolute value function is often used to handle negative values in the integrand. This is because the absolute value function ensures that the output is always positive, which is necessary for calculating the area under the curve.
Double integrals with absolute value functions are commonly used in physics, engineering, and economics to solve problems involving volume, mass, and surface area. They can also be used to calculate the total cost of production or the average value of a function over a given area.