Chapter 8 - Section 8.1 - Arc Length - 8.1 Exercises - Page 549: 23

$L=\int_1^2\sqrt{1+(2x+3x^2)^2}dx=10.0556$

Approximately 10.2, line length, $\sqrt{4+100}=10.2$ $L=\int_a^b\sqrt{1+\Big(\frac{dy}{dx}\Big)^2}dx$ $y=x^2+x^3$ $\frac{dy}{dx}=2x+3x^2$ $a=1$, $b=2$ $L=\int_1^2\sqrt{1+(2x+3x^2)^2}dx=10.0556$