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education/math/MATH1210 (calc 1)/Integrals.md
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@ -157,4 +157,11 @@ $$ L =\int_a^b \sqrt{1 + f'(x)^2} dx$$
1. $L = \int_{-1}^8 \sqrt{1 + (-\frac{5}{12})^2} dx$
2. $= \int_{-1}^8 \sqrt{1 + \frac{25}{144}} dx$
3. = $\int_{-1}^8 \sqrt{\frac{169}{144}}
3. = $\int_{-1}^8 \sqrt{\frac{169}{144}}dx$
4. $= \int_{-1}^8 \frac{13}{12} dx$
5. $\frac{13}{12} x \Big| _{-1}^8$
> Find the distance from the point ${\frac{1}{2}, \frac{49}{48}}$ to the point $(5, \frac{314}{15})$ along the curve $y = \dfrac{x^4 - 3}{6x}$
1. $y' = \dfrac{4x^3(6x) - (x^4 + 3)6}{36x^2}$
2. $= \dfrac{24x^4 -6x^4 - 18}{36x^2}$
3.