# Surface Integral Homework: Is the Author's Solution Wrong?

• fonseh
In summary: Often the author will not state what he wants specifically and you need to experiment a bit to figure it out.
fonseh

## Homework Statement

Is the solution provided by the author wrong ? Stokes theorem is used to calculate the line integral of vector filed , am i right ?

## The Attempt at a Solution

To find the surface integral of many different planes in a solid , we need to use Gauss theorem , right ?

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The author doesn't seem to specify what surface integral he is asking for. If he wants ## \int F \cdot dA ##, Gauss' law works for the surface enclosing a volume, and wouldn't apply here. If he wants you to evaluate ## \int \nabla \times F \cdot \, dA ##, you can use Stokes theorem and alternatively compute the line integral of ## \oint F \cdot \, ds ## around the perimeter. ## \\ ## editing... If the author wants you to evaluate ## \int F \cdot \, dA ##, there are no shortcuts that I know of=neither Gauss' law or Stokes theorem will apply. You simply need to crank it out the long way... And none of us are infallible=it is my guess the author made a mistake.

Last edited:
fonseh
The author doesn't seem to specify what surface integral he is asking for. If he wants ## \int F \cdot dA ##, Gauss' law works for the surface enclosing a volume, and wouldn't apply here. If he wants you to evaluate ## \int \nabla \times F \cdot \, dA ##, you can use Stokes theorem and alternatively compute the line integral of ## \oint F \cdot \, ds ## around the perimeter. ## \\ ## editing... If the author wants you to evaluate ## \int F \cdot \, dA ##, there are no shortcuts that I know of=neither Gauss' law or Stokes theorem will apply. You simply need to crank it out the long way... And none of us are infallible=it is my guess the author made a mistake.
Do you mean that the author maybe mean find the line integral and not find surface integral in this question ?

fonseh said:
Do you mean that the author maybe mean find the line integral and not find surface integral in this question ?
Frequently in such problems the author wants you to demonstrate Stokes' theorem by working it both ways. It's a learning thing.

## 1. Is it necessary to use surface integrals in scientific research?

Surface integrals are often used in scientific research, especially in fields such as physics, engineering, and mathematics. They allow for the calculation of various physical quantities, such as electric and magnetic fields, fluid flow, and heat transfer, which are crucial in understanding and predicting real-world phenomena.

## 2. How do I know if the author's solution to a surface integral is correct?

The best way to determine the correctness of the author's solution to a surface integral is to follow the same steps and methods used in the solution and check your work carefully. It is also helpful to compare the solution to known results or to consult with other experts in the field.

## 3. What are some common mistakes made when solving surface integrals?

Some common mistakes made when solving surface integrals include incorrect application of the formula, not correctly identifying the surface, and computational errors. It is crucial to carefully follow the steps and pay attention to details when solving surface integrals to avoid these mistakes.

## 4. What are some tips for solving surface integrals more efficiently?

To solve surface integrals more efficiently, it is essential to have a strong understanding of the underlying concepts and formulas. It is also helpful to break down the integral into smaller, more manageable parts, and to use symmetry and other properties of the surface to simplify the calculation.

## 5. Are there any software or tools available to help with surface integrals?

Yes, there are various software and tools available that can help with solving surface integrals. Some popular choices include Mathematica, MATLAB, and Wolfram Alpha. These programs have built-in functions and algorithms that can quickly and accurately calculate surface integrals and provide visual representations of the results.

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