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Math Help - Help me with calculus question, due at 12 oclock eastern time!

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    Help me with calculus question, due at 12 oclock eastern time!

    Hi everyone, new to the forums here. I need help on this question ASAP, it's due in less than 15 minutes and I have to submit it online. Here's the question...

    Find the number b such that the line y = b divides the region bounded by the curves y = x2 and y = 9 into two regions with equal area. (Round your answer to the nearest hundredth.)

    Help asap, thank you!
    Nate
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by flairknocks View Post
    Hi everyone, new to the forums here. I need help on this question ASAP, it's due in less than 15 minutes and I have to submit it online. Here's the question...

    Find the number b such that the line y = b divides the region bounded by the curves y = x2 and y = 9 into two regions with equal area. (Round your answer to the nearest hundredth.)

    Help asap, thank you!
    Nate
    Why'd you wait so late?
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  3. #3
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    I've been busy with school band, other homework, etc.
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  4. #4
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by flairknocks View Post
    I've been busy with school band, other homework, etc.
    So...What have you done to try and takle this thing?
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  5. #5
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    I've found the area between the lines, but I don't know how to divide it. I thought it was zero, but then that's x=0. I need y=0, right?
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  6. #6
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by flairknocks View Post
    I've found the area between the lines, but I don't know how to divide it. I thought it was zero, but then that's x=0. I need y=0, right?
    To find the area

    \int_{-3}^{3}(9-x^2)dx

    Then, flip your graph on its side and find the average value...That is

    \frac{1}{9}\int_0^9\sqrt{y}dy
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  7. #7
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by flairknocks View Post
    Hi everyone, new to the forums here. I need help on this question ASAP, it's due in less than 15 minutes and I have to submit it online. Here's the question...

    Find the number b such that the line y = b divides the region bounded by the curves y = x2 and y = 9 into two regions with equal area. (Round your answer to the nearest hundredth.)

    Help asap, thank you!
    Nate
    Area = \int_{-3}^3 9-x^2\,dx = 36. So half the area is 18. You want to find y^2 such that \int_{-y}^y y^2-x^2\,dx = 18.

    Integral equals \left[xy^2-\frac{x^3}{3}\right]_{-y}^y = \frac{4y^3}{3} = 18.

    Therefore y= \left(\frac{27}{2}\right)^{1/3} but remember you want y^2 so the final answer is \boxed{y^2= \left(\frac{27}{2}\right)^{2/3} = 5.67}
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