# Why Is My Integration Approach Not Working?

• Chewy0087
In summary, the conversation is about a problem involving integration and determining the correct form for an expression. The person discussing the problem is having trouble understanding how to get from one step to the next, but ultimately discovers a solution involving changing the integration constant and evaluating the expression at a specific value. They still have some questions about the process and ask for further clarification.
Chewy0087

## Homework Statement

http://i27.photobucket.com/albums/c171/Chewbacc0r/problem.jpg

## The Attempt at a Solution

Basically, for the life of me I can't see how they get from "This expression may be written as..." to "Which may be integrated to contain..."

Now, I have no problem with the integration at all, I just can't see how they've put it in the right form.

Surely;

$$\frac{1}{v_{0}}+\frac{Ct}{m}= \frac{m+Ctv_{0}}{mv_{0}}$$

So $$(\frac{1}{v_{0}}+\frac{Ct}{m})^{-1}=\frac{mv_{0}}{m+Ctv_{0}}$$

Which integrates to;

$$\frac{m}{C}ln(m+Ctv_{0}) + C$$

However as you can see, this is apparently incorrect, and I have a feeling they're right. Just can't see where, I know I'm making a rookie mistake, but I've not practised math for months so it's quite frustrating.

Edit:

I just thought - carrying on using my solution i could simply take $$\frac{m}{C}ln(m)$$ away from both sides, changing the constant, however that feels like such a cop-out to me, though i guess it would work. I'd still like to know how they've done it if anyone knows.

Last edited:
Chewy0087 said:
Surely;

$$\frac{1}{v_{0}}+\frac{Ct}{m}= \frac{m+Ctv_{0}}{mv_{0}}$$

So $$(\frac{1}{v_{0}}+\frac{Ct}{m})^{-1}=\frac{mv_{0}}{m+Ctv_{0}}$$

Which integrates to;

$$\frac{m}{C}ln(m+Ctv_{0}) + C$$

You've somehow identified the integration constant with C. Pick a different symbol and then evaluate the expression at t=0 to identify $$x_0$$.

## 1. What is integration and why is it important in science?

Integration is the process of combining different parts or elements to form a whole. In science, integration allows researchers to connect and understand different concepts or phenomena, and ultimately build a more comprehensive understanding of the natural world.

## 2. What are some common challenges when it comes to integrating different scientific theories or concepts?

One common challenge is finding a way to reconcile conflicting or contradictory evidence or theories. Another challenge is identifying and addressing biases or assumptions that may hinder the integration process.

## 3. How can I improve my skills in integrating different ideas and concepts in science?

One way to improve integration skills is to actively seek out and engage with a diverse range of scientific perspectives and ideas. Additionally, being open-minded and critical in your approach can help you identify connections and patterns that may not be immediately obvious.

## 4. What are some potential benefits of successful integration in scientific research?

Successful integration can lead to a more complete understanding of a particular phenomenon or topic, as well as the development of new theories or ideas. It can also help bridge gaps between different fields and lead to collaborations and advancements in scientific knowledge.

## 5. Are there any potential drawbacks to integration in science?

Sometimes, integration can lead to oversimplification or reductionism, where complex ideas or theories are reduced to a single, unified explanation. It can also be a time-consuming and challenging process, requiring careful analysis and critical thinking. Additionally, successful integration may not always be possible, and accepting uncertainty and ambiguity may be necessary in some cases.

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