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Math Help - area of the region btwn 2 curves - polar coordinates

  1. #1
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    area of the region btwn 2 curves - polar coordinates

    HI

    So the two curves are r = sin x and r = cos x

    The intersecting point is pi/4 which makes r = 1/sq rt 2

    now I know A = 1/2 integral sign (S) a? b? r^2 dx

    The question is what is a and b equal to? I am thinking that b could equal pi/4 and then I can multiply by 2 to get the full area but I don't know how to figure out what a would

    hopefully I have given you all the info you need to help me.

    Thanks

    Calculus beginner
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  2. #2
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    Quote Originally Posted by calcbeg View Post
    HI

    So the two curves are r = sin x and r = cos x

    The intersecting point is pi/4 which makes r = 1/sq rt 2

    now I know A = 1/2 integral sign (S) a? b? r^2 dx

    The question is what is a and b equal to? I am thinking that b could equal pi/4 and then I can multiply by 2 to get the full area but I don't know how to figure out what a would

    hopefully I have given you all the info you need to help me.

    Thanks

    Calculus beginner
    note the symmetry in the graph ...

    A = \int_0^{\frac{\pi}{4}} \sin^2{\theta} \, d\theta

    or ...

    A = \int_{\frac{\pi}{4}}^{\frac{\pi}{2}} \cos^2{\theta} \, d\theta
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  3. #3
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    Now I actually figured out the pi/4 part while I was waiting for someone to guide me but I don't know how you picked the other boundary.

    I was going to use a = c for one b = c for the other and then subtract the area of one from the area of the second to get the overlap..... but obviously I am missing the obvious.

    By the way Skeeter you are my hero in this calculus world. My husband suggests I find out what you would like for Christmas.

    Thanks

    Calculus Beginner
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