# How to calculate a integral on boundary

• Stole
In summary, the conversation is about calculating a specific integration where g(x,y)=0 on \Sigma and \mathbf{n} is the outward pointing unit normal field of the boundary \Sigma. The question is whether the integral equals to 0 in this case. The answer is yes, if the integrand is always 0, the integral will also be 0.
Stole
Hi,
I would like to calculate the following integration:

\oint_{\Sigma}f(x,y)g(x,y)\mathbf{n}\cdot d\mathbf{s}

where g(x,y)=0 on \Sigma, and \mathbf{n} is the outward pointing unit normal field of the boundary \Sigma.

In this case does the integral equals to 0?

Thanks!

Stole said:
Hi,
I would like to calculate the following integration:

$$\oint_{\Sigma}f(x,y)g(x,y)\mathbf{n}\cdot d\mathbf{s}$$

where g(x,y)=0 on$\Sigma$, and [/itex]\mathbf{n}[/itex] is the outward pointing unit normal field of the boundary \Sigma.

In this case does the integral equals to 0?

Thanks!
You forgot the [ tex ] and [ /tex ] tags!
Yes, if your integrand is always 0, the integral is 0. Isn't that obvious?

## What is an integral on boundary?

An integral on boundary is a mathematical calculation that involves finding the area under a curve or surface at the boundary or edge of a given region.

## What is the purpose of calculating an integral on boundary?

The purpose of calculating an integral on boundary is to determine the total amount of a quantity within a given boundary or to find the average value of a function over a specific region.

## What are the different methods for calculating an integral on boundary?

There are several methods for calculating an integral on boundary, including the fundamental theorem of calculus, substitution, integration by parts, and trigonometric substitution.

## How do I know which method to use when calculating an integral on boundary?

The method used to calculate an integral on boundary depends on the specific function and limits of integration involved. It is important to understand the properties of each method and choose the one that best fits the given problem.

## What is the relationship between an integral on boundary and the area under a curve?

An integral on boundary is essentially the calculation of the area under a curve or surface at the boundary of a given region. The two concepts are closely related and can be used interchangeably in many cases.

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