Unraveling the Mystery: How WolframAlpha Got from Step 1 to 2

  • MHB
  • Thread starter Dethrone
  • Start date
  • Tags
    Mystery
In summary, the conversation discussed how WolframAlpha went from step 1 to step 2 in a specific problem. One person was confused about where the extra "two" came from, and the missing 1/sqrt(x) in the "du" term. Another person suggested that they multiplied the outside by two and the inside by 1/2 to get 1, but this still did not fully explain the missing term. The conversation then shifted to a simpler approach of expanding, but one person wanted to practice without using it.
  • #1
Dethrone
717
0
View attachment 1242

How did WolframAlpha get from step 1 to 2?

I don't get where that extra "two" came from (outside of the integral), and I don't get how there is an extra u factored out.

My initial thought was maybe they mutlipled the outside by two, and inside by 1/2 so that equals 1, but it still doesn't account for the missing 1/sqrt(x) to complete "du".
 

Attachments

  • how.JPG
    how.JPG
    38.3 KB · Views: 82
Physics news on Phys.org
  • #2
From

$ du = \frac{1}{2 \sqrt{x}}dx $

We get $ 2 \sqrt{x} \ du = dx $

[tex] 2u \ du = dx [/tex]

Now substitute and pull out the constant 2 ...

:D
 
  • #3
How did I miss that the first time :( The ramifications of doing calculus up all night for fun.
Thanks!
 
  • #4
A simpler approach would be to expand .
 
  • #5
ZaidAlyafey said:
A simpler approach would be to expand .

Very true, but I wanted to practice without it :) Thanks guys!
 

FAQ: Unraveling the Mystery: How WolframAlpha Got from Step 1 to 2

1. What is WolframAlpha?

WolframAlpha is a computational knowledge engine that provides answers to factual questions by computing and analyzing data from various sources. It is not a search engine, but rather a tool for accessing and understanding data.

2. How does WolframAlpha work?

WolframAlpha uses a combination of algorithms, curated data, and natural language processing to understand and answer questions. It breaks down a question into different parts and then searches through its vast database to find relevant data and perform computations to generate an answer.

3. What is the goal of "Unraveling the Mystery: How WolframAlpha Got from Step 1 to 2"?

The goal of "Unraveling the Mystery" is to provide insight into the development and evolution of WolframAlpha, from its initial concept to its current state. It aims to shed light on the challenges and innovations that have led to its success as a computational knowledge engine.

4. What are some key milestones in the development of WolframAlpha?

Some key milestones in the development of WolframAlpha include its initial launch in 2009, the addition of new data and features over the years, and its integration with various platforms such as Siri and Mathematica. The development of its natural language processing capabilities and its expansion into new domains such as finance and health have also been significant milestones.

5. How has WolframAlpha impacted the scientific community?

WolframAlpha has had a significant impact on the scientific community by providing a powerful tool for accessing and analyzing data. It has made it easier for researchers and scientists to obtain accurate and reliable information, perform complex calculations, and explore different datasets. It has also been used in education, helping students and teachers to better understand and visualize concepts in various fields of study.

Similar threads

I Different Substitution for Solving an Integral
Replies
6
Views
655
B How do I invert this exponential function?
Replies
3
Views
3K
B How to set up an integral to integrate over a sine wave?
Replies
2
Views
2K
MHB How to use change of variables technique here?
Replies
2
Views
1K
I Proof of 1/(x^2) Not Having Limit at 0
Replies
5
Views
2K
I How to know if a complex root is inside the unit circle
Replies
5
Views
2K
MHB What is the Mystery Behind the Extra 1/2 in This Integration?
Replies
2
Views
2K
I Where Did I Go Wrong in Deriving Pi Using Calculus?
Replies
6
Views
4K
MHB How Can I Simplify This Integral Using Long Division?
Replies
2
Views
1K
B Calculating shaded area: I'm getting discrepancies between methods
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top