diff --git a/education/math/MATH1210 (calc 1)/Integrals.md b/education/math/MATH1210 (calc 1)/Integrals.md index fc0a915..4a54007 100644 --- a/education/math/MATH1210 (calc 1)/Integrals.md +++ b/education/math/MATH1210 (calc 1)/Integrals.md @@ -178,4 +178,10 @@ $$ L =\int_a^b \sqrt{1 + f'(x)^2} dx$$ 13. $= \frac 1 2 \int_{1/2}^5 (x^2 - x^{-2})dx$: Find the indefinite integral 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. $=(\frac{5000}{240} - \frac{24}{240}) - (\frac{5}{240} - \frac{240}{240})$ \ No newline at end of file +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. $L = \int_{-1}^1 \sqrt{1 + (-\frac{x}{\sqrt{1-x^2}})}$ \ No newline at end of file