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Arc Length

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AP Calculus AB/BC

Definition

The arc length of a curve is the distance along the curve between two points. It measures how long the curve is.

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"Arc Length" also found in:

Subjects (17)

Practice Questions (20+)

Which of the following formulas calculates the arc length of a smooth, planar curve?
What is the arc length of the curve y = x^2, from x = 0 to x = 2?
The arc length of a curve is always _______ the distance traveled along the curve.
Which of the following integrals represents the arc length of the curve y = e^x, from x = 0 to x = 1?
What is the arc length of the curve y = sin(x), from x = 0 to x = π?
If the equation of a curve is given parametrically by x = t^2 and y = t^3, what is the arc length of the curve from t = 0 to t = 1?
The arc length of a curve is always a _______ quantity.
The distance traveled by an object is always _______ the arc length of the curve representing its motion.
The arc length of a curve is always _______ the displacement of an object along the curve.
Which of the following is an application of arc length in real-world scenarios?
The arc length of a curve can be approximated by dividing the curve into _______.
Which of the following integrals represents the arc length of the curve y = ln(x), from x = 1 to x = e?
What is the formula to find arc length for a parametric equation?
Consider the parametric equations: x(t) = t^2 y(t) = 3t What is the arc length of the curve between t = 0 and t = 2?
The parametric equations of a curve are: x(t) = 2cos(t) y(t) = 2sin(t) What is the arc length of the curve between t = 0 and t = π/2?
Consider the parametric equations: x(t) = e^t + e^(-t) y(t) = e^t - e^(-t) What is the arc length of the curve between t = 0 and t = ln(2)?
Consider the parametric equations: x(t) = t^2 - 1 y(t) = t^3 + 2t What is the arc length of the curve between t = -1 and t = 1?
Consider the curve given by the equation y = x^2. What is the arc length of the curve between x = 0 and x = 1?
The curve y = sin(x) is defined over the interval [0, π/2]. What is the arc length of the curve?
For the equation y = ln(x), what is the arc length of the curve between x = 1 and x = e?

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Arc Length

from class:

AP Calculus AB/BC

Definition

"Arc Length" also found in:

Subjects (17)

Practice Questions (20+)

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study guides for every class

that actually explain what's on your next test

Arc Length

from class:

AP Calculus AB/BC

Definition

Related terms

"Arc Length" also found in:

Subjects (17)

Practice Questions (20+)

© 2024 Fiveable Inc. All rights reserved.

AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.

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