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Arc length (mostly a problem with integration)

  • Thread starter Geekchick
  • Start date
1. The problem statement, all variables and given/known data

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

2. Relevant equations

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

3. 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[tex]^{2}[/tex]x so I could plug it into the formula to get [tex]\int^{\frac{\pi}{2}}_{0}[/tex][tex]\sqrt{1+sin^{2}x}[/tex] the problem is when I try to integrate...well i can't. I tried to use substitution but since i don't have cos[tex]^{2}[/tex]x anywhere I had some issues.
 
Anybody? Please this is driving me crazy!
 

djeitnstine

Gold Member
614
0
You can't do it. You have to do a numerical approximation
 

djeitnstine

Gold Member
614
0
I get 1.910098938245763 with wxmaxima
 

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