Question

Parametric area?

Answer 1

I'm unsure as to what the graph would look like for this function from 0 to 8pi and how to set up an integral for D.

Answer 2

I used the formula of a circle and got an area of .727, but I know that can't be right, as it just hit me that it's a fourth of an ellipse.

Answer 3

Were we supposed to learn Parametric area? I thought it was just polar...

Answer 4

@justjm that's probably not the case

Answer 5

I'm almost 100% certain that this equation can be converted into polar, just not sure how.

Answer 6

I used the formula
\[\sqrt{x ^{2}+y ^{2}}=r \] and solved for that integral from 0 to pi/2 times 1/2 to get .727

Answer 7

But I dunno how to convert that in terms of an ellipse.

Answer 8

It's a logarithmic spiral:

\(x^2 + y^2 = r^2 = (e^{-0.1 t} \cos t ) ^2 + (e^{-0.1 t} \sin t ) ^2 \)

So in polar:

\(r = e^{-0.1t}\)

For the area:

Answer 9

Plot is in Desmos

Answer 10

woop woop