Question

Calculating the parametric curve determined by two equations.

Answer 1

\[x = e^{t} \sin(t), y = e^tcos (t)\]

Answer 2

Use the identity:

\(\sin^2 t + \cos^2 t = 1\)

Write sin and cos in terms of x and y

Answer 3

\[\int\limits_{0}^{\pi}\sqrt{e^{2t}[1+\sin(2t)] + e^{2t}[1-\sin(2t)}] dt\]

Answer 4

Why are you integrating it?

Answer 5

Integral formula for calculating arc length? o_O

Answer 6

you can simplify your integrand a little more

Answer 7

e^(2t)*sin(2t)-e^(2t)*sin(2t)=?

Answer 8

\[\sqrt{2}(e^{\pi} - 1)\]