Arc length (mostly a problem with integration)

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Homework Help Overview

The discussion revolves around finding the arc length of the graph of the function f(x) = cos(x) over the interval [0, π/2]. The problem involves the application of integration techniques.

Discussion Character

  • Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to apply the arc length formula by first calculating the derivative of the function and substituting it into the integral. They express difficulty in integrating the resulting expression and mention issues with substitution.

Discussion Status

Some participants are exploring different methods to approach the problem, including numerical approximation. There is a mention of a specific numerical result obtained using wxmaxima, but no consensus on a method for analytical integration has been reached.

Contextual Notes

The original poster indicates challenges with integration techniques and the absence of certain trigonometric identities in their attempts, which may be contributing to the difficulty in solving the problem.

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Homework Statement



Find the arc length oh the graph f(x)=cosx on the integral [0,\frac{\pi}{2}]

Homework Equations



\int^{b}_{a}\sqrt{1+{f'(x)}^{2}}dx

The Attempt at a Solution



Alright so I took the derivative of f(x) to get f'(x)=-sinx then I squared it to get sin^{2}x so I could plug it into the formula to get \int^{\frac{\pi}{2}}_{0}\sqrt{1+sin^{2}x} the problem is when I try to integrate...well i can't. I tried to use substitution but since i don't have cos^{2}x anywhere I had some issues.
 
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Anybody? Please this is driving me crazy!
 
You can't do it. You have to do a numerical approximation
 
I get 1.910098938245763 with wxmaxima
 

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