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Math Help - Areas between curves - Integration

  1. #1
    Junior Member Fnus's Avatar
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    Areas between curves - Integration

    So, I've been trying to do this on my own, but I'm really at a loss.
    (The problem is in the attatched file)

    At first I figured I'd need to find out where the two curves intersect,
    so I did x = \sqrt{k}

    Which I dont even know if right. I sure hope it is!

    Then I figured that the area would go from 0 to \sqrt{k},
    and then I tried to integrate, and substitute x for \sqrt{k}.

    Eventually I ended up with something like 1.8-something which is wrong.

    I'd love for some guidance on this one, thanks in advance!
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  2. #2
    Super Member
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    The graph does intersect at x = \sqrt{k}

    Therefore, the integral is:
    \int_{0}^{\sqrt{k}} k-x^2~dx

    Simply integrate it, and find the area between sqrt(k) and 0. Then set it equal to 2.4 and solve for k. You should be getting k = 2.3489...

    k \sqrt{k} - \frac{\sqrt{k^3}}{3} = 2.4

    \frac{2\sqrt{k^3}}{3} = 2.4

    k = ...

    Your approach is correct, perhaps you might have made a mistake in solving for k or while integrating.
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  3. #3
    Junior Member Fnus's Avatar
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    Okay, thankies.

    At least I was on the right track, Imma just keep doing it 'til I get it right, then.
    I was just afraid I was on the complete wrong track, thanks for clearing it up. (:
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