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Thread: area of the polar curve

  1. #1
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    area of the polar curve

    area of the polar curve-100-1-10.png
    please help with the question
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  2. #2
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    Re: area of the polar curve

    What do you know about this and where do you have trouble? Do you know what a "loop" is? Do you know how to find area when the curve is given in polar coordinates? Do you know how to integrate?
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  3. #3
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    Re: area of the polar curve



    $\theta=0 \implies r=3$ ... from there, half a loop is formed at the first value of $\theta > 0$ where $r=0$.
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  4. #4
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    Re: area of the polar curve

    I know how to integrate, but i cannot understand the statement of the question.
    About the polar coordinates, i have only deal with circle and oval.
    I've try to draw the picture but it doesn't help me solve it.
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  5. #5
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    Re: area of the polar curve

    Attached is a graphical depiction of the hint I gave you in post #3 ...

    area of one whole loop, $\displaystyle A = 2 \int_0^{\theta_1} \dfrac{r^2}{2} \, d\theta$

    where $\theta_1$ is the first angle greater than $\theta = 0$ where $r = 0$
    Attached Thumbnails Attached Thumbnails area of the polar curve-polar1.png  
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