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Registered: 10/28/02
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Math Question
    #2767055 - 06/05/04 10:07 PM (14 years, 15 days ago)

Hello I have a math question. This question shouldnt be that hard, but there is no example in my book to explain it, so frankly I dont see how I am supposed to know what to do.
Use Green's Theorem to compute the area of the region inside the path c(t) = (cos(t)cos(2t), sin(t)cos(2t)) -pi/2<=t<=pi/2

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Registered: 07/21/01
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Re: Math Question [Re: TheCow]
    #2768470 - 06/06/04 10:43 AM (14 years, 15 days ago)

"Green's Theorem is a form that the fundamental theorem of calculus takes in the context of integrals over planar regions."

basically just integrate c(t) from -pi/2 to pi/2
giving ....
area within region = c'(-pi/2) - c'(pi/2)

you get to integrate.

ive found Mathematica to be quite helpful for calc and differential equations but dont rely on your calculator or computer to integrate etc. calculus should be able to be done in your head and plugging in numbers (the last thing) can be done on a calc to save time and to ensure no lower math errors

If you're frightened of dying and you're holding on.you'll see devils tearing your life away.
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Registered: 10/28/02
Posts: 4,790
Last seen: 9 years, 11 months
Re: Math Question [Re: Eightball]
    #2768862 - 06/06/04 02:21 PM (14 years, 14 days ago)

Thankyou. What I ended up doing was taking the x part and multiplying it by the derivative of the y part. Then I took the y part and multiplied it by the derivative of the x part. I then subtracted them and simplified. At which point I believe I got sin(2x)^2. I then integrated and plugged in my limits and took half of that since its the area, getting pi/4.

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