Chapter 8.1, Problem 1PT

A definite integral for the length of y = x³, 1 ≤ x ≤ 2 is

1. a) ${\displaystyle {\int }_1^2\sqrt{1+x^3}dx}$
2. b) ${\displaystyle {\int }_1^2\sqrt{1+x^6}dx}$
3. c) ${\displaystyle {\int }_1^2\sqrt{1+9x^4}dx}$
4. d) ${\displaystyle {\int }_1^2\sqrt{1+3x^2}dx}$