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Math Help - [SOLVED] Calculus Help

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    Last edited by Marg7; January 5th 2010 at 02:35 AM.
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    Quote Originally Posted by Marg7 View Post
    Consider the curve y^2=4+x and chord AB joining points A(-4, 0) and B(0,2) on the curve.

    start by making a sketch of the parabola and chord ...

    1. Find the x- and y-coordinates of the point on the curve where the tangent line is parallel to chord AB.

    set the slope of AB = derivative of the curve, solve.

    2. Find the area of the region R enclosed by the curve and chord AB.

    find the equation of line AB, y = mx+b

    \textcolor{red}{A = \int_{-4}^0 (upper \, curve) - (mx+b) \, dx}

    3. Find the volume of the solid generated when the region R, defined in part 2., is revolved about the x-axis.

    method of washers ...

    \textcolor{red}{V = \pi \int_{-4}^0 (upper \, curve)^2 - (mx+b)^2 \, dx}
    ...
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