The integration problem below was submitted by a student who needs help to solve it.
Can you solve the problem?
Here it is:
Prove that \(\large
\begin{align} \int_0^1 \sqrt{\frac{\log(1/t)}{t}} \,\mathrm{d}t = \sqrt{2\pi} \end{align}\)
-
- Active Topics
-
-
- by Eli 4 hours ago Re: What is in Your Mind? View the latest post Replies 673 Views 273185
- by Eli 9 hours ago Iran Launches Retaliatory Attack Against Israel View the latest post Replies 18 Views 404
- by Eli 10 hours ago Programmatically Move Files from One Folder to Another View the latest post Replies 6 Views 1268
- by Eli 1 day ago Russia Invades Ukraine View the latest post Replies 644 Views 209912
- by Forbidden_Technology 1 day ago All in One: YouTube, TED, X, Facebook and Instagram Reels, Videos, Images and Text Posts View the latest post Replies 312 Views 8193
- by Eli 6 days ago Collection of Greatest Christian Hymns of all Times View the latest post Replies 33 Views 43382
- by Eli 1 week ago What is Retrieval-Augmented Generation (RAG)? View the latest post Replies 2 Views 213
- by Eli 1 week ago Chat With ChatGPT - An Interactive Conversational AI View the latest post Replies 22 Views 24070
- by Eli 2 weeks ago Christian Podcasts View the latest post Replies 5 Views 28575
- by Eli 2 weeks ago Pondering Big Cosmology Questions Through Lectures and Dialogues View the latest post Replies 33 Views 45302
-
Calculus: Integration
-
- Expert Member
- Reactions: 23
- Posts: 55
- Joined: 7 years ago
- Has thanked: 14 times
- Been thanked: 28 times
- Contact:
Assumptions:
A()=A(), where A is the area under the curve.
Knowledge:
Integration by substitution,
Integration by parts,
There is Gauss error function that i used, if there are some other methods then someone else may share them as well. This function will help us to 'end' the integration whenever we reach to integrate such function below, we will substitute with 'erf' function.
Note: erf has standard values for zero and infinity, the values can be proved in matlab console, type erf(0) and erf(1/0)
=
=
The procedure:
In case of errors, then suggestions are open. May be mods will try to put this in a good mathematical typesetting.
A()=A(), where A is the area under the curve.
Knowledge:
Integration by substitution,
Integration by parts,
There is Gauss error function that i used, if there are some other methods then someone else may share them as well. This function will help us to 'end' the integration whenever we reach to integrate such function below, we will substitute with 'erf' function.
Note: erf has standard values for zero and infinity, the values can be proved in matlab console, type erf(0) and erf(1/0)
=
=
The procedure:
In case of errors, then suggestions are open. May be mods will try to put this in a good mathematical typesetting.
0
-
- Information
-
Who is online
Users browsing this forum: No registered users and 0 guests