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xz_007 [3.2K]
3 years ago
10

Find the work done by the force field f in moving an object from a to

Mathematics
1 answer:
elixir [45]3 years ago
6 0
Presumably the path from a to b is a line segment, in which case we can parameterize it by

\mathbf r(t)=(1-t)(1,1)+t(4,9)=(1+3t,1+8t)

with 0\le t\le1. Then the work done along this path - denoted by \mathcal C - is

\displaystyle\int_{\mathcal C}\mathbf f\cdot\mathrm d\mathbf r=\int_{t=0}^{t=1}(6(1+8t)^{3/2},9(1+3t)(1+8t))\cdot(3,8)\,\mathrm dt
=\displaystyle\int_0^1(72(1+3t)(1+8t)+18(1+8t)^{3/2})\,\mathrm dt
=\dfrac{6309}5
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