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m_a_m_a [10]
3 years ago
14

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

Mathematics
1 answer:
SOVA2 [1]3 years ago
5 0
Assuming the path from a to b is a line segment, we can parameterize it by
\mathbf r(t)=(1-t)(1,1)+t(3,9)=(1+2t,1+8t)=(x(t),y(t))
for 0\le t\le1. Then the work done by \mathbf f(x,y) along this path, which I'll denote \mathcal C, is
\displaystyle\int_{\mathcal C}\mathbf f(x,y)\cdot\mathrm d\mathbf r=\int_{t=0}^{t=1}f(x(t),y(t))\cdot(2,8)\,\mathrm dt=\displaystyle\int_0^1(2(1+8t)^{3/2},3(1+2t)(1+8t))\cdot(2,8)\,\mathrm dt=\displaystyle4\int_0^1(1+8t)^{3/2}\,\mathrm dt+24\int_0^1(1+10t+16t^2)\,\mathrm dt
=\dfrac{242}5+272=\dfrac{1602}5
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