- #1
reinloch
- 5
- 0
Homework Statement
Suppose we walk along a unit semicircle.
Homework Equations
Find the average value of our distance from the base of the semicircle.
The Attempt at a Solution
[itex] y_{ave} = \frac{1}{1-(-1)}\int_{-1}^1\sqrt{1-x^2}\ dx = \frac{\pi}{4} [/itex]
OR
[itex] y = \sin\theta, \qquad 0 \le \theta \le \pi[/itex]
[itex] y_{ave} = \frac{1}{\pi-0}\int_0^{\pi}\sin\theta\ d\theta = \frac{2}{\pi} [/itex]
I would appreciate if anyone can enlighten me on why these approaches lead to different answers, and if anyone of them is wrong. Thanks.