# How does one do the following Integral.

• Quantumpencil
In summary: But if it's difficult to do one way, do the difficult way. In summary, the problem is to find the flux due to a point charge at the center of a cube.
Quantumpencil

## Homework Statement

The problem is really not bad; It's to find the flux due to a point charge at the center of Cube of side length d. I've gotten the answer I believe using Gauss's law (q/6epsilon)

I tried doing a Flux integral, and the integral seems kind of a pain in the ***... I'm not sure how to do it. I will post where I'm at and hopefully someone can tell me how to integrate this.

the exact question was

"Find the flux through a face of a cube from a point charge at the cube's center"

## The Attempt at a Solution

First I chose the face, assuming the charge is at the origin, such that da=dzdy(x), x = d/2, and y and z vary from -d/2 to d/2. I then changed Coulombs law to Cartesian coordinates and did some dot products, and substituted in d/2 for x.

$$\int[\frac{Q(d/2)}{(d^2/4)+y^2+z^2)^{3/2}}dydz$$

How can one integrate this?

Last edited:
Please write down the question exactly as it was given to you. An electric field can not have dimensions of q/epsilon (a flux can). And please be more clear in your working - write full equations instead of fragments. Right now, one can only guess what you are trying to calculate.

Yeah, don't know why I typed Electric field, the problem is to find

$$\int(E)\cdot da$$, the flux through the surface.

If you already figured out the flux using Gauss' law and symmetry, why do you need to do the painful integral?

I mean, I just usually try to work problems multiple ways. If the integral isn't do-able then I suppose I won't, but often times I just don't think of the proper tricks to solve integrals and things, and doing problems that was as well keeps my bank of problem solving knowledge sharper.

I'm sure you probably can do it. But I think the lesson learned would be disproportionate to the effect involved. If it's easy both ways, do it both ways. If it MUCH easier one way stick with that one.

## 1. How do I solve an integral?

To solve an integral, you need to use integration techniques such as substitution, integration by parts, or partial fractions. First, identify the type of integral you have (e.g. definite, indefinite, improper) and then choose the appropriate technique to solve it. Make sure to follow the correct steps and use algebraic manipulation to simplify the integral before integrating.

## 2. What is the difference between definite and indefinite integrals?

A definite integral has specific limits of integration, meaning you are finding the area under the curve between two points. An indefinite integral does not have limits and instead gives you the general antiderivative of a function. In other words, a definite integral gives a numerical value while an indefinite integral gives a function.

## 3. Can I use a calculator to solve integrals?

Yes, there are many online calculators and computer programs that can help you solve integrals. However, it is still important to understand the underlying concepts and techniques behind integration to check the accuracy of the calculator's answer and to apply it to more complex integrals.

## 4. How do I know if my answer to an integral is correct?

You can check your answer by taking the derivative of the antiderivative you found. If the result is the original function, then your answer is correct. You can also use online tools and graphing calculators to graph both the original function and its antiderivative and see if they match up.

## 5. Are there any special cases or exceptions in solving integrals?

Yes, there are some special cases such as integrals involving trigonometric functions, logarithmic functions, and inverse trigonometric functions. In these cases, there are specific integration techniques and formulas that can be used. It is important to familiarize yourself with these special cases to effectively solve integrals.

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