Question

did i do something wrong here????

Evaluate the line integral ∫CF⋅dr, where F(x,y,z)=4sinxi+4cosyj−xzk and C is given by the vector function r(t)=t^6i−t^5j+t^4k , 0≤t≤1.

Answer 1

did \[\int\limits_{0}^{1}<4\sin(t^6), 4\cos(-t^5), (t^6t^4)> \dot <6t^5, -5t^4, 4t^3>\]

equals\[\int\limits_{0}^{1}(24t^5\sin(t^6)-20t^4\cos(-t^5)+4t^(13) dt \]

plug that into a calculator and i get -1.24 and webwork says no. did i make a mistake somwhere?

Answer 2

well, first, is it a dot product?

Answer 3

yes. i didn't know how to do a dot in the thing, so i just wrote dot.

Answer 4

it's r(t) dot r'(t)

Answer 5

try ` -1.813`

Answer 6

yes, that works. what did i goof on?

Answer 7

look at ur z component after parameterization

Answer 8

oops. -x, so -(t^6). i knew it was something simple like that. thanks!

Answer 9

adhd makes my brain work faster than my pencil sometimes and i miss negatives....:D

Answer 10

he found it faster than me

Answer 11

you're using wolfram right ? i think there is some wolfram applet for line integrals too
http://www.wolframalpha.com/input/?i=%5Cint_0%5E1+%2824t%5E5%5Csin%28t%5E6%29-20t%5E4%5Ccos%28-t%5E5%29%2B4t%5E%2813%29%29++dt

Answer 12

no, i was using integral-calculator.com. but i can use wolfram too

Answer 13

Why not do it by hand?

Answer 14

faster, fibonaccichick. i know how to integrate and some of these end up being really long integrals, so it's just faster once i get the integral set up.

Answer 15

XD I know, but usually you are not allowed to use calculators on tests (at least for my calc 3) so it's good practice

Answer 16

oh yeah, the tests have easier integrals than the webwork gives us though.

Answer 17

for the test it'll be something like the integral of x +y or sin+cos instead of all this garbledy gook.

Answer 18

lol

Answer 19

ahhh ok, yea, If you have a TI 89 you can nicely do the integral on it :) but yes, this is nasty, very nasty. Side note, why in the j component did you keep a negative on the t^5? I thought vecotors were supposed to be wriiten I-j+k, so we would have to modify the sign? (It's been like 3 years since calc 3 for me)

Answer 20

actually, no not that nasty: here it's just two u substitutions

Answer 21

yeah they are cookedup to evaluate nicely by hand

Answer 22

yeah, we only have like 50 minutes to do 10 questions, so they make them shorter. :D thanks for all the help! onto question 8!

Answer 23

it becomes \[\int _{0}^{1} 4sinu-4cosu-4t^{13}\]

Answer 24

with implied du's and dt's

Answer 25

it also leaves less room for mistakes for me. with my adhd, it's common for me to do stuff like that. as seen here. on a test once my teacher circled where i'd accidentally done 1-0=-9 and put a question mark next to it. he only took off 1 point cause even though i got the wrong answer cause of that goof, i still knew what i was doing. working to try and slow down my brain so i don't goof like that again

Answer 26

well, on homework yes, but you will never get better without practice

Answer 27

hi