Chapter 16.2, Problem 3PT

A definite integral for ${\displaystyle {\int }_{C}F\cdot dr}$, where $F\left(x,y\right)=x^{2}i+y^{2}j$ and C is the line from (1, 0) to (0, 1) given by x = 1 – t, y = t, $t\in \left[0,1\right]$, is:

1. a) ${\displaystyle {\int }_0^1\left(2t-1\right)dt}$
2. b) ${\displaystyle {\int }_0^1\left(t^2+{\left(1-t\right)}^2\right)dt}$
3. c) ${\displaystyle {\int }_0^1\left(t^3+{\left(1-t\right)}^{2}t\right)dt}$
4. d) ${\displaystyle {\int }_0^{1}2dt}$