arc length formula
s = rθ
The arc length formula is used to calculate the length of a curve, or arc, on a function. It’s also known as the arc length formula for a smooth curve.
The formula for arc length is given by:
arc length = ∫ (a to b) √[1 + (dy/dx)²] dx
Here, a and b are the lower and upper limits of the interval where the curve is defined. dy/dx is the derivative of the function y with respect to x.
This formula can be used for any curve, as long as the curve is smooth. A curve is considered smooth if it has no abrupt changes in direction or slope.
To use this formula, you need to find the derivative of the function and square it. Then, add 1 to the result, and take the square root of the sum. Finally, integrate the resulting expression from a to b.
The arc length formula is very useful in many different fields, such as physics, engineering, and mathematics, where it helps to find the length of curves, trajectories, and other shapes.
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