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education/math/MATH1210 (calc 1)/Integrals.md

@@ -179,3 +179,9 @@ $$ L =\int_a^b \sqrt{1 + f'(x)^2} dx$$
 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. $L = \int_{-1}^1 \sqrt{1 + (-\frac{x}{\sqrt{1-x^2}})}$