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Problem 26 Medium Difficulty

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

$ \displaystyle \int_C z \ln (x + y) \, ds $, where $ C $ has parametric equations $ x = 1 + 3t $, $ y = 2 + t^2 $, $ z = t^4 $, $ -1 \leqslant t \leqslant 1 $

Answer

$1.72599$

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Video Transcript

so again similar to the past few problems style. Set it up and and leave it to you to use a calculator to compare the last t integral. So dx DT is three d u i d t his two t DZ DT. It's for T Cube. The so DSS should be squared of nine plus everything square added together 40 square plus 16 t to six and gt So this in the growth should be t goes from negative 1 to 1 z is t to the fourth X plus y should be t square plus three t process three and, uh, the S is these things, and you can use a calculator to finish that.