Chapter 15 - Section 15.2 - Vector Fields and Line Integrals: Work, Circulation, and Flux - Exercises - Page 838: 19

$\dfrac{1}{2}$

Here, we have: $ \dfrac{dr}{dt}=i+2t j+k$ The work done can be computed as: $W=\int_a^b F(r(t)) \dfrac{dr}{dt}(dt) $ or, $=\int_0^{1} (t^3 i+t^2 t j-t^3 k)\cdot (i+2t j+k) dt $ or, $=\int_0^1 t^3+2t^3 -t^3 \ dt$ or, $= 2\times \int_0^1 t^3 \ dt$ or, $= [\dfrac{t^4}{2}]_0^1 $ or, $=\dfrac{1}{2}$