Determine the line integral for the field $F(x,y) = (xy,y^2)$, when $\gamma(t)= (t,t^2)$ and $t \in [0,1].$
I have that $$\int_\gamma F \cdot ds = \int_{0}^{1} F(\gamma(t)) \cdot \gamma'(t) \ dt = \int_{0}^{1} (t^3, t^4) \cdot (1,2t) \ dt = \int_{0}^{1}t^3 +2t^5 \ dt = \frac{7}{12}$$
however, I'm not sure if I should compute $$\int_{0}^{1} F(\gamma(t)) \cdot \gamma'(t) \ dt$$ or $$\int_{0}^{1} F(\gamma(t)) \cdot \|\gamma'(t)\| \ dt$$
?