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education/math/MATH1210 (calc 1)/Integrals.md
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@ -184,4 +184,9 @@ $$ L =\int_a^b \sqrt{1 + f'(x)^2} dx$$
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. $L = \int_{-1}^1 \sqrt{1 + (-\frac{x}{\sqrt{1-x^2}})}$
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. $\arcsin($