Finding the value of the integral on this t-shirt

In summary, the conversation centers around a joke t-shirt worn by Dr. Ben Goertzel that includes a mathematical integral problem. Various individuals attempt to solve the problem and arrive at different answers before realizing that there is a typo on the shirt. Ultimately, the correct answer is determined to be approximately 0.5273, with the mistake being a minus sign that should have been a plus sign.
  • #1
rugerts
153
11
Hello all,
I was watching some random videos on YouTube and found one of Dr. Ben Goertzel (a leading expert in the field of AI) and he was wearing the t shirt you see below. It caught my attention. I tried working it out, but I had no luck as it got messy fast. I then tried throwing it into Wolfram as well as another calculator and found an answer of 0.38. Is this correct? I would have thought that the answer would've 1/2, 1, or something along these lines to make sense of the joke.
To anyone who can work this out or explain it... thank you!
Here's Dr. Goertzel wearing the shirt as well as an enlarged view of the shirt itself.
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  • #2
Hint: That looks like its begging for some trigonometric substitution ...
 
  • #3
guesses anyone?
 
  • #4
Hahah I believe the shirt has a typo!

I did the integral (it’s really not difficult with the right substitution) and the answer is certainly not 1/2

HOWEVER, I noticed, if the upperbound was 2/√π instead of √(2/π), then the answer would be 1/2

Kind of embarrassing! But maybe I’m just a glass ##_0\int^{\frac{2}{\sqrt{\pi}}}(...)dx## empty kind of guy. :DD
 
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Likes FactChecker, PeroK and rugerts
  • #6
Though I notice, too, that we can keep the limits as specified on the shirt, but change the left-most minus sign into a plus, and we'll again arrive at the 0.5 figure. Well, very close to it. :cool:
 
  • #7
Hiero said:
Hahah I believe the shirt has a typo!

I did the integral (it’s really not difficult with the right substitution) and the answer is certainly not 1/2

HOWEVER, I noticed, if the upperbound was 2/√π instead of √(2/π), then the answer would be 1/2

Kind of embarrassing! But maybe I’m just a glass ##_0\int^{\frac{2}{\sqrt{\pi}}}(...)dx## empty kind of guy. :DD
Very nice! I think you got it. Thanks so much.
 
  • #8
0.5273
 

1. What is an integral?

An integral is a mathematical concept that represents the area under a curve in a graph. It is used to find the total value or quantity of a function over a given interval.

2. How do you find the value of an integral?

The value of an integral can be found by using integration techniques such as substitution, integration by parts, or using a table of integrals. It involves breaking down the function into smaller parts and finding the area under each part.

3. What is the significance of finding the value of an integral on a t-shirt?

Finding the value of an integral on a t-shirt is a fun and creative way to showcase a mathematical concept. It can also serve as a conversation starter or a way to express one's interest in math and science.

4. Can you explain the process of finding the value of an integral in simpler terms?

To find the value of an integral, you need to first understand the function and its graph. Then, you break down the function into smaller parts and find the area under each part. Finally, you add up all the areas to get the total value of the integral.

5. What are some real-life applications of finding the value of an integral?

Integrals are used in various fields such as physics, engineering, economics, and statistics. Some examples of real-life applications include calculating the work done by a force, finding the velocity of an object, determining the cost of production, and analyzing data in research studies.

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