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Math Help - double and triple integration

  1. #1
    ggw
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    double and triple integration

    i have couple problems, it took me an hour, but I haven't found a way to solve it. Can anyone better help ?

    see my attach pictures, some problems need to see the figure. thanks a lot
    Attached Thumbnails Attached Thumbnails double and triple integration-reviewprob.jpg  
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  2. #2
    ggw
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    i thought someone can help me

    I review (pretest drill) which i posted and no one help me. If you don't want to do it because you can't write the Latax in here. You also didn't help me with any clues. So sad...
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  3. #3
    Senior Member ecMathGeek's Avatar
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    Quote Originally Posted by ggw View Post
    I review (pretest drill) which i posted and no one help me. If you don't want to do it because you can't write the Latax in here. You also didn't help me with any clues. So sad...
    Perhaps no one helped because we cannot read the problem.
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  4. #4
    ggw
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    A. consider the region R in the first quarant that is outside the circle r=1 and inside the four-leaved rose r = 2sin2theta.
    a) draw sketch of the circle and four-leaved rose and the shade the region R.
    b) write the following double integral as an iterated in polar coordinates. Do not evaluate.
    double integral of cos 2thetadA (see picture attached)

    c). evaluate the integral...i can do this part.

    B. consider the following iterated integral

    Double integral of ydxdy ( limit respect to y from -4 to 0, limit integral respect to x from -sqrt(16-y^2) to sqrt(16-y^2)

    b1. sketch the region of integration
    b2. rewrite the integral in order dydx


    your help will distribute a lot of to my math skills. Thanks for your help....!
    b3. rewrite the integral in polar coordinates
    b4. evaluate
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  5. #5
    ggw
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    i posted it for a while and no one helps me at all. hic hic...at least give me a direction so I can start from it.
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  6. #6
    Senior Member ecMathGeek's Avatar
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    Quote Originally Posted by ggw View Post
    A. consider the region R in the first quarant that is outside the circle r=1 and inside the four-leaved rose r = 2sin2theta.

    a) draw sketch of the circle and four-leaved rose and the shade the region R.
    I assume you know how to sketch figures in polar coordinates.

    b) write the following double integral as an iterated in polar coordinates. Do not evaluate.
    double integral of cos 2thetadA (see picture attached)
    I will represent (theta) as O
    INT cos(2O) dA = Int Int cos(2O)*r dr dO

    c). evaluate the integral...i can do this part.

    B. consider the following iterated integral

    Double integral of ydxdy ( limit respect to y from -4 to 0, limit integral respect to x from -sqrt(16-y^2) to sqrt(16-y^2)

    b1. sketch the region of integration
    b2. rewrite the integral in order dydx
    The domain of this integration is of the bottom half of a circle (if I'm not mistaken). The radius of this circle is 4 and the center is at the origin. The function that we are integrating, f(x,y) = y is a flat plane in 3D space that bisects the y-z axis. You'll have to do your best to try and draw this because I cannot do a 3D graph on this site (that I know of).

    The integral can be rewritten in the order dy dx by changing the domain of integration to D = {(x,y) | -4 <= x <= 4, -sqrt(16 - x^2) <= y <= 0}

    Int{x = -4, 4} INT{y = -sqrt(16 - x^2), 0} y dy dx

    (I could be mistaken on this. It's been a while since I've done a problem like this.)

    your help will distribute a lot of to my math skills. Thanks for your help....!
    b3. rewrite the integral in polar coordinates
    b4. evaluate
    D = {(r,O) | 0 <= r <= 4, -pi <= O <= 0}
    dy dx = dA = r dr dO
    rsinO = y
    rcosO = x

    Int{O = -pi, 0} Int{r = 0, 4} rsinO*r dr dO
    = Int{O = -pi, 0} Int{r = 0, 4} r^2*sinO dr dO
    Last edited by ecMathGeek; April 26th 2007 at 10:14 AM.
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  7. #7
    ggw
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    how would you set up the limit of integral for polar coordinate in part A (a3) ? Thanks for your help....!
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