Calculating the Length of a Curve with Calculus

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SUMMARY

The discussion focuses on calculating the length of the curve defined by the polar equation r = √(1 + cos(2θ)) over the interval π/2 ≤ θ ≤ π/2. The user successfully simplified the equation to r = √2 * cos(θ) and applied the integral formula for arc length, resulting in a final answer of √2 * π. The user expresses confidence in their algebraic manipulation, although they humorously caution against potential errors.

PREREQUISITES
  • Understanding of polar coordinates and equations
  • Knowledge of calculus, specifically integration techniques
  • Familiarity with the arc length formula in polar coordinates
  • Basic algebra skills for simplification of expressions
NEXT STEPS
  • Study the derivation and application of the arc length formula in polar coordinates
  • Practice solving similar problems involving polar curves and integration
  • Explore advanced calculus topics such as parametric equations and their lengths
  • Review common algebraic mistakes in calculus to improve accuracy
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Students preparing for calculus exams, educators teaching polar coordinates, and anyone interested in mastering the calculation of curve lengths using integration techniques.

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Homework Statement


i'm studying for an exam. and I'm pretty sure i know how do do these types of problems. this is aneven problem in the book so i wanted to know if my answer is right.

Find the length of the curve for [tex]r=\sqrt{1+\cos2\theta} , \pi/2\leq\theta\leq\pi/2[/tex]

Homework Equations



integral of [tex]\sqrt{(r^2+(dr/d\theta)^2}[\tex]<br /> <br /> <h2>The Attempt at a Solution</h2><br /> i simplified my r to be [tex]\sqrt{2}*\cos\theta[/tex]<br /> after simplification and plugging into the formula. i got my answer to be [tex]\sqrt{2}*\pi[/tex][/tex]
 
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I got the same result. I'm known for making tons of algebra mistakes, so trust my algebra at your own risk. :-p
 

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