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Problem 25 Medium Difficulty

Use a calculator to evaluate the line integral correct to four decimal places.

$ \displaystyle \int_C xy \arctan z \, ds $, where $ C $ has parametric equations $ x = t^2 $, $ y = t^3 $, $ z = \sqrt{t} $, $ 1 \leqslant t \leqslant 2 $

Answer

$94.8231$

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Video Transcript

so I'll set it up for you and you get you some The calculator to computer last into growing tea. So the X ditty is t t y eighty iss Really square did he is one over two teeth and that one over two So yes, should be square root off all these everything square on DTV So we have forty square we have nine t force. We have one over four Peter, the negative waas So one over fourteen. Okay, so teach you go from one to two x Why should be teacher of the Fifth and hark tension Z should be squared up t and the things and that you can use your cooperator to estimate this.