Compute the length of the arc of the curve from point P to point Q. x^2 = (y - 8)^3, P(1, 9),...
Question:
Compute the length of the arc of the curve from point {eq}P {/eq} to point {eq}Q {/eq}.
{eq}x^2 = (y - 8)^3, \; P(1, 9), \; Q(27, 17) {/eq}
Arc length of a Curve:
To solve this problem we will use the following theorem:
The arc length of a curve y = f(x) on the interval {eq}\left[ a,b \right] {/eq} is given by
{eq}L = \int_a^b \sqrt{1 + (y^{'})^{2}} \, dx {/eq}
Answer and Explanation: 1
Become a Study.com member to unlock this answer! Create your account
View this answerGiven:
a = 1 and b= 27
{eq}(y-8)^{3} = x^{2} \Rightarrow y - 8 = x^{\frac{2}{3}} \Rightarrow y = x^{\frac{2}{3}} + 8 {/eq}
Derivative of y with...
See full answer below.
Learn more about this topic:
from
Chapter 12 / Lesson 12To determine the arc length of a function, integration can be used to determine the arc length over a specified interval. Learn about arc lengths and discover how to set up integrals to determine the arc length of a function over a specified interval.