I am trying to 'use an integral in polar coordinates to calculate the area enclosed by this curve':

The curve is: r=sin2θ, θ ∈ [0, π] which I believe is already in polar form.

I plotted it as:

PolarPlot[ Sin[2θ], {θ, 0, π}]

I have looked in several places at possible way to find area, but it seems that there's a ton of ways to do it. I have seen people talk about regions, booles, approximate areas, solve, etc...and have only found myself getting confused and jumbled up when I try to enter in my own problem.

There are two things I am looking to do with this curve. First is to find the area enclosed by the curve. Then I want to find the length of the curve. But, first things first, I am trying to figure out the area first.

I hope this is specific enough.

Thanks in advance for your help

I am trying to 'use an integral in polar coordinates to calculate the area enclosed by this curve':

The curve is: $r=\sin 2\theta$, $\theta \in [0, \pi]$ which I believe is already in polar form.

I plotted it as:

PolarPlot[Sin[2θ], {θ, 0, π}]

I have looked in several places at possible way to find area, but it seems that there's a ton of ways to do it. I have seen people talk about regions, booles, approximate areas, solve, etc...and have only found myself getting confused and jumbled up when I try to enter in my own problem.

There are two things I am looking to do with this curve. First is to find the area enclosed by the curve. Then I want to find the length of the curve. But, first things first, I am trying to figure out the area first.

I hope this is specific enough.

Thanks in advance for your help

I am trying to 'use an integral in polar coordinates to calculate the area enclosed by this curve':

The curve is: r=sin2θ, θ ∈ [0, π] which I believe is already in polar form.

I plotted it as: PolarPlot[ Sin[2[Theta]], {[Theta], 0, [Pi]}]

[![The Plot][1]][1] [1]: https://i.sstatic.net/baKDV.png

I have looked in several places at possible way to find area, but it seems that there's a ton of ways to do it. I have seen people talk about regions, booles, approximate areas, solve, etc...and have only found myself getting confused and jumbled up when I try to enter in my own problem.

There are two things I am looking to do with this curve. First is to find the area enclosed by the curve. Then I want to find the length of the curve. But, first things first, I am trying to figure out the area first.

I hope this is specific enough.

Thanks in advance for your help

I am trying to 'use an integral in polar coordinates to calculate the area enclosed by this curve':

The curve is: r=sin2θ, θ ∈ [0, π] which I believe is already in polar form.

I plotted it as:

PolarPlot[ Sin[2θ], {θ, 0, π}]

I have looked in several places at possible way to find area, but it seems that there's a ton of ways to do it. I have seen people talk about regions, booles, approximate areas, solve, etc...and have only found myself getting confused and jumbled up when I try to enter in my own problem.

There are two things I am looking to do with this curve. First is to find the area enclosed by the curve. Then I want to find the length of the curve. But, first things first, I am trying to figure out the area first.

I hope this is specific enough.

Thanks in advance for your help