- #1
mugzieee
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i got a problem that says:
x=sqrt(5)sin2t -2
y=sqrt(5)cos2t - sqrt(3)
how would i go about starting it?
x=sqrt(5)sin2t -2
y=sqrt(5)cos2t - sqrt(3)
how would i go about starting it?
[tex] :(1): \ \ \ \ (CurveLength_{t=a}^{t=b}) = \int_{a}^{b} \sqrt { (\frac {dy} {dt})^2 + (\frac {dx} {dt})^2} \ \ dt [/tex]mugzieee said:i got a problem that says:
x=sqrt(5)sin2t -2
y=sqrt(5)cos2t - sqrt(3)
how would i go about starting it?
To find the length of a curve, you will need to use a mathematical formula called the arc length formula. This formula takes into account the equation of the curve and the limits of integration to calculate the length of the curve.
The arc length formula is L = ∫√(1+(dy/dx)^2) dx, where dy/dx is the derivative of the curve's equation. This formula is derived from the Pythagorean theorem and is used to calculate the length of a curve between two points.
Yes, the arc length formula can be used to find the length of any curve, as long as its equation is known and can be differentiated. This formula can be applied to both simple and complex curves.
First, you need to find the derivative of the curve's equation. Then, plug the derivative into the arc length formula and set the limits of integration to the start and end points of the curve. Integrate the formula to get the length of the curve. Finally, round the result to the desired number of decimal places to get the final answer.
Finding the length of a curve is important in many fields of science and engineering. It can help in determining the distance between two points on a curve, the amount of material needed to create a curved object, or the amount of force required to navigate along a curved path. Additionally, it is a fundamental concept in calculus and can help in solving more complex problems involving curves.