# How to Calculate the Arc Length of x^1/2

• andryd9
In summary, the formula for calculating the arc length of x^1/2 is L = ∫√(1 + (dy/dx)^2)dx, where dy/dx represents the derivative of the function. The derivative of x^1/2 can be found by using the power rule of differentiation. Integration is necessary to find the total length of a curve, and the limits of integration depend on the range of x values. This formula can be applied to other differentiable functions with appropriate limits of integration.
andryd9
So sorry if this has been discussed elsewhere before. I know it may be trivial but for some reason I just can't get it. I simply can't seem to integrate the square root of (1 + 1/4x). This problem has been highlighted for a reason, but I'm missing the point. Any input is much appreciated.

Hi andryd9!

$$u=\sqrt{1+\frac{1}{4x}}$$

Alternatively, you might want to calculate the arc length of x2. It should have the same value!

Thank you for the help:)

## 1. What is the formula for calculating the arc length of x^1/2?

The formula for calculating the arc length of x^1/2 is given by L = ∫√(1 + (dy/dx)^2)dx, where dy/dx represents the derivative of the function.

## 2. How do you find the derivative of x^1/2?

The derivative of x^1/2 can be found by using the power rule of differentiation, which states that the derivative of x^n is nx^(n-1). In this case, n = 1/2, so the derivative is 1/2x^(-1/2).

## 3. Can the arc length of x^1/2 be calculated without using integration?

No, the arc length of x^1/2 cannot be calculated without using integration. Integration is necessary to find the total length of a curve, which is what the arc length represents.

## 4. How do you choose the limits of integration for calculating the arc length of x^1/2?

The limits of integration depend on the range of x values over which the arc length is to be calculated. Typically, the lower limit is the starting point of the curve and the upper limit is the ending point of the curve.

## 5. Can the formula for calculating the arc length of x^1/2 be applied to other functions?

Yes, the formula for calculating the arc length of x^1/2 can be applied to other functions as long as the function is differentiable and the limits of integration are properly chosen.

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