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Math Help - Area between 3 curves?

  1. #1
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    Area between 3 curves?

    So I'm finding this problem difficult:

    What is the area of the region in the first quadrant (upper right quadrant) bounded by the curves y = sin(x)cos^2(x), y = 2xcos(x^2), and y = 4 4x?

    I keep trying it, and graphing it on my calculator but I'm getting different answers every time. Sometimes I'll get around .38 other times I get 1.8 I'm not sure what I'm doing wrong and what I should be getting?

    Thanks for your help!
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  2. #2
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    Re: Area between 3 curves?

    Area between 3 curves?-clipboard01.jpg

    solve

    $$2x_c\cos(x_c^2)=4-4x_c$$

    and solve

    $$\sin(x_d)\cos^2(x_d)=4-x_d$$

    then the area of the bounded region becomes

    $$\int_0^{x_c}\left(2 x \cos(x^2)-\sin(x)\cos^2(x)\right) dx+\int_{x_c}^{x_d}\left((4-4x)-\sin(x)\cos^2(x)\right)dx$$
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  3. #3
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    Re: Area between 3 curves?

    Quote Originally Posted by canyouhelp View Post
    So I'm finding this problem difficult:

    What is the area of the region in the first quadrant (upper right quadrant) bounded by the curves y = sin(x)cos^2(x), y = 2xcos(x^2), and y = 4 4x?

    I keep trying it, and graphing it on my calculator but I'm getting different answers every time. Sometimes I'll get around .38 other times I get 1.8 I'm not sure what I'm doing wrong and what I should be getting?
    Have a look at this.
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  4. #4
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    Re: Area between 3 curves?

    I got 3.78718. Is this close?
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  5. #5
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    Re: Area between 3 curves?

    Quote Originally Posted by Plato View Post
    I got 3.78718. Is this close?
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  6. #6
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    Re: Area between 3 curves?

    It doesn't look like it.

    Area between 3 curves?-clipboard01.jpg
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  7. #7
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    Re: Area between 3 curves?

    Quote Originally Posted by romsek View Post
    It doesn't look like it.

    Click image for larger version. 

Name:	Clipboard01.jpg 
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    I don't really understand what that is saying (I'm not used to working problems out online) Doesn't it say once it's fully integrated it's about .378... Like what I ended up with? Or is it saying something else?
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  8. #8
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    Re: Area between 3 curves?

    Oh my gosh! Nevermind, I just realized I wrote it out wrong. I meant .378... not 3.78! Sorry. Now I see!
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