Finding Arc Length of f(x) = (4-x^2)^(1/2)

Thread starter ruri
Start date Oct 9, 2008
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Arc Arc length Length

In summary, the formula for finding arc length is L = ∫√(1 + (f'(x))^2)dx. To calculate the arc length of a function, you need to take the integral of the square root of 1 plus the square of the derivative of the function with respect to x. The purpose of finding arc length is to measure the distance along a curve or a portion of a curve. The arc length of a function cannot be negative, as it represents a physical distance. However, there are limitations to using the arc length formula. It can only be used for smooth, continuous functions and cannot be applied to functions with sharp corners or discontinuities. Additionally, the function must be defined over a finite interval

Oct 9, 2008

ruri

Homework Statement

What is the arc length of f(x) = (4-x^2)^(1/2)?

Homework Equations

The Attempt at a Solution

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Oct 9, 2008

Defennder

Homework Helper

Just use the formula for arc length. And take note of the endpoints of the arc. You can get those from inspection.

FAQ: Finding Arc Length of f(x) = (4-x^2)^(1/2)

What is the formula for finding arc length?

The formula for finding arc length is: L = ∫√(1 + (f'(x))^2)dx

How do you calculate the arc length of a function?

To calculate the arc length of a function, you need to take the integral of the square root of 1 plus the square of the derivative of the function with respect to x.

What is the purpose of finding arc length?

The purpose of finding arc length is to measure the distance along a curve or a portion of a curve. This can be useful in many real-world applications, such as calculating the length of a road or the circumference of a circle.

Can the arc length of a function be negative?

No, the arc length of a function cannot be negative. It represents a physical distance and therefore must be a positive value.

Are there any limitations to using the arc length formula?

Yes, there are limitations to using the arc length formula. It can only be used for smooth, continuous functions and cannot be applied to functions with sharp corners or discontinuities. Additionally, the function must be defined over a finite interval for the formula to be applicable.