Find The Length Of The Curve. R(T) = 4T, T2, 1 6 T3 , 0 ≤ T ≤ 1
- Choose the equation that describes the curve.
- Integrate the equation.
- Substitute the limits of integration.
- Calculate the length of the curve.
Finding the Length of a Curve
Calculating the length of a curve can be useful in a variety of circumstances. In this article, we will use the equation r(t) = 4t, t2, and 1 – 6t3 to find the length of the curve for 0 ≤ t ≤ 1.
Steps to Find the Length of a Curve
Calculating the Length of the Curve
The equation we are using to find the length of the curve is r(t) = 4t, t2, and 1 – 6t3 for 0 ≤ t ≤ 1.
We can find the length of the curve by integrating the equation and then substituting the limits of integration. The integral of the equation is:
L = ∫01√[(4t)2 + (t2)2 + (1 – 6t3)2]dt
We can now calculate the length of the curve by substituting the limits of integration:
L = ∫01√[(4t)2 + (t2)2 + (1 – 6t3)2]dt = 2.12
Therefore, the length of the curve with the equation r(t) = 4t, t2, and 1 – 6t3 for 0 ≤ t ≤ 1 is 2.12.