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Math Help - integral

  1. #1
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    integral

    find the value of ( b ) so that the line y=b divides the region bound by the graph of the tow functions f(x)= 9-x^2 , g(x)=0 into regions of equal area
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  2. #2
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    Quote Originally Posted by BAHADEEN View Post
    find the value of ( b ) so that the line y=b divides the region bound by the graph of the tow functions f(x)= 9-x^2 , g(x)=0 into regions of equal area
    What have you tried to solve this?
    Last edited by mr fantastic; December 31st 2010 at 04:32 PM.
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    sorry, i have not idea to solve
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  4. #4
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    Quote Originally Posted by BAHADEEN View Post
    sorry, i have not idea to solve
    start by calculating the area of the region between y = 9-x^2 and the x-axis ... you'll need that piece of information to find the "half" area.

    what do you get?
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  5. #5
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    the area of the region between f(x)=9-x^2 and the x-axis equal 36
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  6. #6
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    Quote Originally Posted by BAHADEEN View Post
    the area of the region between f(x)=9-x^2 and the x-axis equal 36
    good, then let y = b be the horizontal line that cuts the region's area in half.

    using symmetry, note that the area of the region in quadrant I is \displaystyle \int_0^3 9 - x^2 \, dx = 18

    since y = 9-x^2 , x = \sqrt{9-y} , and ...

    \displaystyle \int_0^b \sqrt{9-y} \, dy = 9

    evaluate the integral and solve for b
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