# Arc length (mostly a problem with integration)

#### Geekchick

1. The problem statement, all variables and given/known data

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

2. Relevant equations

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

Related Calculus and Beyond Homework News on Phys.org

#### Geekchick

Anybody? Please this is driving me crazy!

#### djeitnstine

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

#### djeitnstine

Gold Member
I get 1.910098938245763 with wxmaxima

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving