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martinhiggs
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Homework Statement
[tex]\frac{dz}{d\theta}[/tex] = [tex]\int\sqrt{a^{2} + z'^{2}}[/tex]
I think I would have to make a substitution but I'm not sure which one to make...
How would I integrate the following:
- Thread starter martinhiggs
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In summary, integration is a mathematical process used to find the anti-derivative of a function, which can then be used to calculate the definite integral. There are two types of integration: definite and indefinite, and the method used depends on the complexity of the function. Not all functions can be easily integrated, and integration is used in many fields to solve real-world problems and analyze data.
[tex]\frac{dz}{d\theta}[/tex] = [tex]\int\sqrt{a^{2} + z'^{2}}[/tex]
I think I would have to make a substitution but I'm not sure which one to make...
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tiny-tim
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Welcome to PF!
Hi martinhiggs! Welcome to PF!
(have a theta: θ and a square-root: √ and an integral: ∫)
I'm confused
…
What is z' ? And what is the d(something) inside the ∫ ?
Hi martinhiggs! Welcome to PF!
(have a theta: θ and a square-root: √ and an integral: ∫
)I'm confused
…What is z' ? And what is the d(something) inside the ∫ ?
Related to How would I integrate the following:
How would I integrate the following:
The following are the 5 most frequently asked questions about integration:
1. How do I integrate a function?
To integrate a function, you use a mathematical process called integration, which involves finding the anti-derivative of the given function. The anti-derivative can then be used to calculate the definite integral.
2. What is the difference between definite and indefinite integration?
Definite integration involves finding the exact numerical value of the integral within a specific interval, while indefinite integration involves finding the anti-derivative of a function without any specified limits.
3. How do I know which method of integration to use?
There are several methods of integration, such as substitution, integration by parts, and partial fractions. The method you choose depends on the complexity of the function and the specific rules you need to apply to solve it. It is important to have a strong understanding of all the methods and when to use them.
4. Can I integrate any function?
Not all functions can be easily integrated. Some functions, like trigonometric functions, require special techniques to integrate. In some cases, it may not be possible to find an explicit solution to the integral, and numerical methods may be used instead.
5. How is integration used in real life?
Integration is used in many fields, such as physics, economics, and engineering, to solve real-world problems. It is used to calculate areas, volumes, and other physical quantities. It is also used in finance to calculate the total profit or loss over a period of time. Additionally, integration is used in data analysis to find patterns and trends in large datasets.
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