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

  • Context: MHB 
  • Thread starter Thread starter Dethrone
  • Start date Start date
  • Tags Tags
    Mystery
Click For Summary

Discussion Overview

The discussion revolves around understanding the steps taken by WolframAlpha in a specific calculus problem, particularly focusing on the transition from one step to another in the context of integration and substitution methods.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant expresses confusion about the appearance of an extra "two" outside of the integral and the factoring of an additional "u".
  • Another participant explains the relationship between the differential and the substitution, indicating how to derive the expression for dx from du.
  • A third participant reflects on their oversight in understanding the steps, attributing it to a lack of sleep after a night of studying calculus.
  • One participant suggests that a simpler approach would be to expand the expression, though they acknowledge their preference for practicing without that method.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best approach to the problem, with some advocating for simplification while others prefer to tackle it through substitution. The discussion remains unresolved regarding the optimal method.

Contextual Notes

There are indications of missing assumptions regarding the steps taken in the integration process, and the discussion does not fully resolve the mathematical intricacies involved.

Who May Find This Useful

Students and individuals interested in calculus, particularly those grappling with integration techniques and substitution methods.

Dethrone
Messages
716
Reaction score
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: 120
Physics news on Phys.org
From

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

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

2u \ du = dx

Now substitute and pull out the constant 2 ...

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

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

Similar threads

High School How do I invert this exponential function?
  • · Replies 3 ·
Replies
3
Views
4K
High School How to set up an integral to integrate over a sine wave?
  • · Replies 2 ·
Replies
2
Views
2K
MHB How to use change of variables technique here?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Proof of 1/(x^2) Not Having Limit at 0
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad How Does WolframAlpha Calculate the Sum of (2n+1)/(n(n+1)(n+2))?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Having trouble understanding a seemingly simple u-substitution
  • · Replies 5 ·
Replies
5
Views
2K
MHB Solve ln(x-1)/x-3=2 | Step-by-Step Guide
  • · Replies 6 ·
Replies
6
Views
3K
MHB How Can I Simplify This Integral Using Long Division?
  • · Replies 2 ·
Replies
2
Views
1K
MHB What is the Mystery Behind the Extra 1/2 in This Integration?
  • · Replies 2 ·
Replies
2
Views
2K
High School Calculating shaded area: I'm getting discrepancies between methods
  • · Replies 3 ·
Replies
3
Views
3K