Question

Evaluate the area enclosed by the curve corresponding to the following parametric equations:

x(t) = sin(3t)
y(t)=2cos(3t)-1

0<=t<= pi/2

What to use to solve this question and how to do so ?

Answer 1

There might be another way but you can try writing the parametric equations as one first

Answer 2

We use :

A = integral from a to be 2pi f(x) ( arc length ) dt ??

because if so I think it isn't included in the final exam so no need to worry about it :D

Answer 3

integral sqrt( (dx/dt)^2 + (dy/dt)^2 ) dt

Answer 4

Isn't that the arc length ?

Answer 5

i think so

Answer 6

but he asked for the area ?

Answer 7

I think it's A = integral from a to be 2pi f(x) ( arc length ) dt ,,, but if this is it then it's not included , but I want to make sure if this is it first :D

Answer 8

here http://tutorial.math.lamar.edu/Classes/CalcII/ParaArea.aspx

Answer 9

To be honest I've never seen this formula :D

If he was asking for the arc length this it would be the upper half of the circle I think , but I'm used to questions like this :

find the arc length of .... , but in this case he asked for the area , but I'm not sure if it's like what I said than its not included , if he's asking for the arc length then the formula is like your said. That's why I'm asking , sorry for that :(