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2 changed files with 1 additions and 39 deletions

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@ -1,27 +0,0 @@
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@ -179,14 +179,3 @@ $$ L =\int_a^b \sqrt{1 + f'(x)^2} dx$$
14. $= \dfrac{1}{2} (\frac{1}{3}x^3 - x^-1)\Big|_{1/2}^5$ : Plug and chug
15. $= (\frac{125}{6} - \frac{1}{10}) - (\frac{1}{48} - 1)$
16. $=(\frac{5000}{240} - \frac{24}{240}) - (\frac{5}{240} - \frac{240}{240})$
> Find the length of the curve $y = \sqrt{1 - x^2}$
1. $y$ has a domain of $[-1, 1]$
2. $y' = \dfrac{1}{2}(1-x^2)^{-1/2}(-2x)$
3. $= -\dfrac{x}{\sqrt{1 - x^2}}$
4. $L = \int_{-1}^1 \sqrt{1 + (-\dfrac{x}{\sqrt{1-x^2}})^2}dx$
5. $L = \int_{-1}^1 \sqrt{1 + \dfrac{x^2}{1-x^2}}dx$
6. $L = \int_{-1}^1 \sqrt{\dfrac{1}{1-x^2}}dx$
7. $L = \int_{-1}^1 \dfrac{1}{\sqrt{1-x^2}}dx$
8. $L = \arcsin(x) \Big|_{-1}^1$
9. $\arcsin($