EVOXDRIFTER5685 EVOXDRIFTER5685

26-10-2017
Mathematics

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Find the length of the curve. r(t) = 3 i + t2 j + t3 k, 0 ≤ t ≤ 1

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LammettHash LammettHash

27-10-2017

Call the curve [tex]C[/tex], then the length of [tex]C[/tex] is given by the line integral

[tex]\displaystyle\int_C\mathrm dS=\int_{t=0}^{t=1}\|\mathbf r'(t)\|\,\mathrm dt=\int_{t=0}^{t=1}t\sqrt{9t^2+4}\,\mathrm dt=\frac{13\sqrt{13}-8}{27}[/tex]

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