How do I integrate this function for finding the arch length of a curve?

In summary, the conversation is about finding the arch length of a curve using the integral $\int_0^b \sqrt{1+sh^2(x/a)} dx$. There is confusion about the terminology used, specifically the word "count" and the meaning of "sh". It is clarified that "sh" refers to the hyperbolic sine and its derivative is cosh. The conversation ends with the confirmation that the problem has been solved and the use of the given equation for the next step.
  • #1
Madou
42
0
I'm finding the arch length of a curve:
[tex] $\int_0^b \sqrt{1+sh^2(x/a)} dx$ [/tex]
How do i integrate this function?
 
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  • #2
What do you mean by "count"?
What is "sh"?
If it is the hyperbolic sine: cosh^2 - sinh^2 = 1.
 
  • #3
I think he meant "evaluate".
CompuChip said:
What do you mean by "count"?
 
  • #4
The derivative of sinh is cosh and the derivative of cosh is sinh
 
  • #5
klondike said:
I think he meant "evaluate".
It's a pity I can't edit the topic.
 
  • #6
Madou said:
The derivative of sinh is cosh and the derivative of cosh is sinh

Exactly. Does this mean you have solved the problem?
 
  • #7
CompuChip said:
Does this mean you have solved the problem?

Next step was to use the equation CC gave me.
Thank you, guys.
 

FAQ: How do I integrate this function for finding the arch length of a curve?

1. What is an integral?

An integral is a mathematical concept that represents the area under a curve on a graph. It is often used to find the total amount or quantity of something, and is an important tool in calculus and other branches of mathematics.

2. How do you count an integral?

To count an integral, you must use a method known as integration, which involves breaking the area under the curve into smaller, more manageable pieces and finding the sum of these pieces. This can be done using different techniques, such as the fundamental theorem of calculus or substitution.

3. Why is counting an integral important?

Counting an integral is important because it allows us to find the total amount or quantity of something that is changing continuously, such as velocity, acceleration, or volume. It also has many real-world applications in fields such as physics, engineering, and economics.

4. What are the different types of integrals?

There are two main types of integrals: definite and indefinite. Definite integrals have specific limits of integration and give a single numerical value as the result, while indefinite integrals do not have limits and give a general formula with a constant of integration as the result.

5. How can integrals be applied in real life?

Integrals have many practical applications in different fields. For example, in physics, integrals can be used to calculate the work done by a force or the amount of energy stored in a system. In economics, integrals can be used to find the total revenue or profit function for a business. They can also be used in engineering to calculate the area under a stress-strain curve to determine the strength of a material.

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