## anonymous 4 years ago find the length: x=e^tcos t y=e^tsin t. t is betw 0 and 2

1. anonymous

hahha. if i were the real bieber do u think i would calll myself liliy and would i actually be smart enough to find this site and do math qs?

2. anonymous

to find the curve you do sqaure root of(dx/dy)^2+ (dy/dx)^2)

3. anonymous

ya?

4. Australopithecus

are you looking for distance between y values?

5. anonymous

holy crap. DO nOT!!! come into MY QUESTION and write a whole long question like this. please open ur open question and i will be glad to help u out with these:)

6. anonymous

@liliy :o i did :P and no one answered it and theres only 4 questions but there not bath there career education .-.

7. anonymous

fine. im a nice person so ill help: but its really not fair what u did. A,A,A,D

8. anonymous

;p I'm sorry ill delete mine

9. anonymous

relax, its fine

10. anonymous

im just saying having it in ur own question is better.

11. anonymous

(also you can legit just google the questions)

12. anonymous

i did lmfao and I couldn't find any thing thats why I'm here

13. anonymous

alright:). well i hope i helped

14. anonymous

with what o.O?

15. anonymous

i just gave u the answers : 1.A 2.A 3.A 4.D

16. anonymous

:O

17. anonymous

@liliy thanks :O

18. anonymous

to find length of the parametric curve you need to integrate over the arc length of the curve $\int\limits_{}^{}\sqrt{dx^{2} +dy^{2}}$ to factor in variable t, multiply by dt/dt $\int\limits_{0}^{2}\sqrt{\frac{dx^{2} +dy^{2}}{dt^{2}}} dt$ which can be written as $\int\limits_{0}^{2}\sqrt{(\frac{dx}{dt})^{2} +(\frac{dy}{dt})^{2}} dt$ $\frac{dx}{dt} = e^{t}(\cos t -\sin t)$ $\frac{dy}{dt} = e^{t} (\sin t + \cos t)$ $\rightarrow \sqrt{2}\int\limits_{0}^{2}e^{t} dt$

19. anonymous

wait, i dont undestand ur last step. wat happend to the sin and cos?

20. anonymous

plug in the expressions for dx/dt and dy/dt , square them and combine terms when you do that you notice that sin^2 + cos^2 = 1 , and the rest of the sin and cos terms cancel so it simplifies to that nice easy integral i have above

21. anonymous

dx/dt is subtracting betw the cos and sin, so it doesnt cancel out!