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wolverine [178]
3 years ago
14

Find the length of l on the curve r(t)=5cos(3t)i-5sin(3t)j+3tk over the interval [3,7]

Mathematics
1 answer:
stealth61 [152]3 years ago
4 0
\mathbf r(t)=5\cos3t\,\mathbf i-5\sin3t\,\mathbf j+3t\,\mathbf k
\mathrm d\mathbf r(t)=\mathbf r'(t)\,\mathrm dt=(-15\sin3t\,\mathbf i-15\cos3t\,\mathbf j+3\,\mathbf k)\,\mathrm dt

\displaystyle\int_C\mathrm d\mathbf r(t)=\int_{t=3}^{t=7}\|\mathbf r'(t)\,\mathrm dt\|=\int_{t=3}^{t=7}\sqrt{225\sin^23t+225\cos^23t+9}\,\mathrm dt
=\displaystyle3\sqrt{26}\int_{t=3}^{t=7}\mathrm dt
=12\sqrt{26}
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