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Math Help - Surface Area (Calculus)

  1. #1
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    Surface Area (Calculus)

    I'm getting confused on this problem, such as when to use dy and dx. If someone can please help me solve these problems and explain them, I would greatly appreciate it. Thank you.

    Find the surface area generated by revolving the region bounded by the curve y = -x^2 + 5 and in the first quadrant about the
    a) y-axis
    b) x-axis
    c) line x = -1
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  2. #2
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    Quote Originally Posted by turtle View Post
    I'm getting confused on this problem, such as when to use dy and dx. If someone can please help me solve these problems and explain them, I would greatly appreciate it. Thank you.

    Find the surface area generated by revolving the region bounded by the curve y = -x^2 + 5 and in the first quadrant about the
    a) y-axis
    b) x-axis
    c) line x = -1
    The surface area rotating about the x-axis is given by:
    2\pi \int_a^b f(x)\sqrt{1+[f'(x)]^2}dx
    But the formula for rotating about the y-axis is not taught.
    However is you really want to, you can think of:
    y=-x^2+5
    As, (rotate graph counterclickwise)
    x=-y^2+5
    Thus,
    y = \sqrt{5-x} \mbox{ on }[0,5]
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