Arc length (mostly a problem with integration)

In summary, the conversation discusses finding the arc length of f(x)=cosx on the interval [0,\frac{\pi}{2}] using the formula \int^{b}_{a}\sqrt{1+{f'(x)}^{2}}dx. The individual attempted to solve the problem but encountered difficulties with integration. Another participant suggests using a numerical approximation instead. The final result obtained is 1.910098938245763 with wxmaxima.
  • #1
Geekchick
77
0

Homework Statement



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

Homework Equations



[tex]\int^{b}_{a}[/tex][tex]\sqrt{1+{f'(x)}^{2}}[/tex]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[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.
 
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  • #2
Anybody? Please this is driving me crazy!
 
  • #3
You can't do it. You have to do a numerical approximation
 
  • #4
I get 1.910098938245763 with wxmaxima
 

Related to Arc length (mostly a problem with integration)

1. What is arc length?

Arc length is the length of a curve or a portion of a curve. It is the distance along the curve from one endpoint to another. It is often calculated using integration.

2. How is arc length calculated?

Arc length can be calculated using integration by dividing the curve into small segments and finding the length of each segment. The lengths of these segments are then added together to get the total arc length.

3. What is the formula for calculating arc length?

The formula for calculating arc length is L = ∫√(1+(dy/dx)^2) dx, where L is the arc length, dy/dx is the derivative of the function, and the integral is taken over the interval of the curve.

4. What is the difference between arc length and arc measure?

Arc length is a physical measurement of the distance along a curve, while arc measure is the angle subtended by an arc at the center of a circle. Arc length is measured in units of length, while arc measure is measured in degrees or radians.

5. How is arc length used in real-life applications?

Arc length is used in a variety of real-life applications, such as calculating the distance traveled by a moving object, finding the circumference of a circle, determining the shape of a curved road, and calculating the length of a cable or wire.

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