Find arc length starting from P_0

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    Arc Arc length Length
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Discussion Overview

The discussion focuses on finding the arc length function for the curve defined by the equation $y=2x^{3/2}$, starting from the point $P_{0}(1,2)$. Participants explore the necessary steps to set up the integral for arc length, including determining the limits of integration.

Discussion Character

  • Homework-related

Main Points Raised

  • One participant asks how to find the arc length function and presents their initial work, including the derivative $y'=3\sqrt{x}$ and the integral $\int_{a}^{b} \sqrt{9x+1}\,dx$.
  • Another participant clarifies that the starting point $P_0$ corresponds to a specific $x$ value, suggesting that this value should be used as the lower limit of integration, $a$.
  • It is noted that the end point is unspecified, allowing for the upper limit of integration, $b$, to remain variable.
  • One participant confirms that the integration should be performed from $1$ to $x$.

Areas of Agreement / Disagreement

Participants generally agree on the approach to finding the arc length, with some clarification on the limits of integration. However, the discussion does not resolve the specifics of the upper limit.

Contextual Notes

The discussion does not address potential assumptions regarding the domain of $x$ or the behavior of the curve beyond the specified starting point.

Who May Find This Useful

Students or individuals interested in calculus, specifically in understanding arc length calculations and integral setup.

ineedhelpnow
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find the arc length function for the curve $y=2x^{3/2}$ with starting point $P_{0}(1,2)$. how do i do this? this is what I've done so far.

$y'=3\sqrt{x}$

$1+(3\sqrt{x})^2=9x+1$

$\int_{a}^{b} \ \sqrt{9x+1},dx$

what's my a and what's my b?
 
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ineedhelpnow said:
find the arc length function for the curve $y=2x^{3/2}$ with starting point $P_{0}(1,2)$. how do i do this? this is what I've done so far.

$y'=3\sqrt{x}$

$1+(3\sqrt{x})^2=9x+1$

$\int_{a}^{b} \ \sqrt{9x+1}\,dx$

what's my a and what's my b?

Hi ineedhelpnow!

Please start new questions in new threads rather than tagging them onto existing threads. As you can see I have moved your question to a new thread.The beginning of the curve is specified as the point $P_0$. Which $x$ corresponds to it? That is your $a$.

The end point is not specified, so we can leave it as $b$, meaning we get an arc length that is a function of $b$.
 
ooookay! thanks! so i do it from 1 to x?
 
ineedhelpnow said:
ooookay! thanks! so i do it from 1 to x?

Yep.
 

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