Problem 14 Medium Difficulty
Evaluate the line integral, where $ C $ is the given curve.
$ \displaystyle \int_C y \, dx + z \, dy + x \, dz $,
$ C: x = \sqrt{t} $, $ y = t $, $ z = t^2 $, $ 1 \leqslant t \leqslant 4 $
Answer
$\left(\frac{8}{3}+\frac{64}{3}+\frac{128}{5}\right)-\left(\frac{1}{3}+\frac{1}{3}+\frac{4}{5}\right)$
Topics
Vector Calculus
Discussion
Top Calculus 3 Educators
Lily A.
Johns Hopkins University
Anna Marie V.
Campbell University
Samuel H.
University of Nottingham
Joseph L.
Boston College
Watch More Solved Questions in Chapter 16
Video Transcript
evaluate this line to grow, so we just have tickles. Won't want to. Four wise t X is one over two square root of TD thes t square The wise DT Xs square of t disease to tt so one, two, four This is one over to t to the one over two plus t Square Prostitute to the This should be three over to TT and we find the entire derivative t to the Stree Over to community property to over three. Four t to the Cube over three. Tito the five over to beautify by two over five in front. So for over five, then we probably before we had for the Israel with Who's eight for Cuba's sixty four four to the five over two is to to the fifth Power, which is thirty two thirty two times for his uh, one twenty eight minus one over three plus one over three plus four or five and you're left with fractions. Simplification, which I think I've had. Leave it to you. So I'll have to open another page
Topics
Vector Calculus
Top Calculus 3 Educators
Lily A.
Johns Hopkins University
Anna Marie V.
Campbell University
Samuel H.
University of Nottingham
Joseph L.
Boston College
