Question

Evaluate the line integral (9x+7y^3) ds, where the curve C is r(t) = (t-9)i + tj, 0<=t<=1.

I'm thinking I input the boundaries of t into r(t) and the put them into the integral...? I will follow and give medal!

Answer 1

The integral looks like this: \[\int\limits_{C}^{}(9x+7y^3)ds\]

Answer 2

I agree

Answer 3

you can do this in a number of ways.

if you note that \(r(t) = <t-9, t>\), then you can see that \(x = t-9, y = t\)

so \(y = x+9\)

that takes you straight into Cartesian, so you can use \(ds = \sqrt{y'^1 + 1 } \; dx\)

Answer 4

or you can follow the paramaterisation route. maybe that is what you are learning as it seems to be quite an endemic ... try both :-)

Answer 5

Oh yeah. His response is better cause when you break it down, you get your answer like I am doing in my notebook right now

Answer 6

I've got it!!!

Answer 7

So ds = \[\sqrt{y+1}\]?

Answer 8

I know the answer guys, if you want it

Answer 9

sorry , bad typo

\(ds = \sqrt{\color{red}{(y')^2} + 1 } \; dx\)

and \(y' = 1\) as \(y = x+9\)

Answer 10

Ah okay, so ds = sqrt(2)

Answer 11

bye0

Answer 12

bye

Answer 13

or you can paramaterise

so you have \(ds = \sqrt{\dot x ^2 + \dot y ^2} \; dt\)

you should get the same answer, try it

Answer 14

Okay, thank you very much, Irish

Answer 15

You guys don't need help so i'm going to go I was going to explain how i got the answer that I got and break it down for you guys so you can understand a little better but you are ignoring me so see yah later

Answer 16

Ignorers:p

Answer 17

well, army, come back if it crashes.

morgan, no offense was intended, seriously. post your solution & ideas, pls.

Answer 18

I'm going to stay only if you need my help

Answer 19

ok

Answer 20

Well, I sorta agree with you so I just realized what you wrote so yeah. Sorry for being rude. I agree with Irish

Answer 21

That's what I can see to use as a system for the whole thing like you can detect whether the st

Answer 22

I meant whether the system will need to use a dialect sinatrical order or not

Answer 23

IDK how to spell sinatrical

Answer 24

me neither, lol!! 🍀

Answer 25

hahaha

Answer 26

i don't even know what it means :p

Answer 27

Hold on a sec... I think it mae

Answer 28

*means

Answer 29

It means a polytheistic term of a function in the math category that can differ whether something can be evaluated by a separatism or not.
Weird, huh!

Answer 30

It's awfully confusing