Compute the work done by the force field along the curve C, where C is the portion of from to .

Question

Compute the work done by the force field  along the curve C, where C is the portion of  from  to  .

Quizplus · Accepted Answer

We need to compute the line integral of the given force field along the curve C. Parametrize C as r(t) = , 0<=t<=1. Then, dr/dt = <1, 2, 1> and the line integral becomes ∫_C (11eaa88b_929d_d892_a696_610fbc1cdcda_TB5869_11) . dr = ∫_0^1 (11t^8, 11t^5, 11t^2) . <1, 2, 1> dt (substituting r(t) and dr/dt) = ∫_0^1 (11t^8 + 22t^5 + 11t^2) dt (dot product and simplification) = (11/9)t^9 + (22/6)t^6 + (11/3)t^3 |_0^1 = 11/9 + 11 + 11/3 = (11*17)/9 = 11eaa88b_929e_4dc8_a696_c909a0094b68_TB5869_11 Hence, the correct answer is (C).

Compute the Work Done by the Force Field Along