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Math Help - Area/Volume between Curves

  1. #1
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    Area/Volume between Curves

    I'm trying to help my sister out with a calc problem that she has in her study guide, and I no longer remember how to do these. Any help is appreciated (and i'm doing this somewhat off memory)

    There are two curves in question: y = 3^x+1 , and y = 5-2x^2
    Region M is defined below 3^x+1 and to the left of 5-2x^2, also bounded by x=0 and y=0.
    Region N is defined as the section between the two curves.

    The questions ask:
    1. Find the area of M and N.
    2. Find the volume of the solid generated when the region N is rotated about the x-axis.

    Thank you
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  2. #2
    MHF Contributor
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    What's the first curve? y = 3^{x+1} or y = 3^{x}+1?

    In either case, you will need to find the points of intersection. This may not be a particularly trivial task.

    I'm not quite sure what "to the left of" means. Maybe a short quiz will help.

    Is the point (0.2,4) in the shaded region?
    Is the point (0.4,3) in the shaded region?
    Is the point (0.6,2) in the shaded region?
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  3. #3
    Senior Member DeMath's Avatar
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    I think, you made a typo in the equation of the first curve, and it should be \mathsf{y=3x+1}
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