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Math Help - Volume of revolution and integration

  1. #1
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    Volume of revolution and integration

    a) Find the volume of the solid formed when the area bounded by the curve y = 1/(3x+4), the coordinate axes and the line x=2 is rotated one complete revolution about the x-axis.
    b) Evaluate the integral of f(x) between 3 and -3
    WHEN f(x) = x+1 (when x<1) and f(x) = 2x (when x >(and equal to) 1)
    I am unsure how to complete these two questions, any help is greatly appreciated, thank you
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  2. #2
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    Quote Originally Posted by christina View Post
    a) Find the volume of the solid formed when the area bounded by the curve y = 1/(3x+4), the coordinate axes and the line x=2 is rotated one complete revolution about the x-axis.
    b) Evaluate the integral of f(x) between 3 and -3
    WHEN f(x) = x+1 (when x<1) and f(x) = 2x (when x >(and equal to) 1)
    I am unsure how to complete these two questions, any help is greatly appreciated, thank you
    to a): The rotation volume with the x-axis as axis of rotation is calculated by:

    V_{rot} = \int_a^b(\pi \cdot y^2)dx

    In your case a = 0 and b = 2

    To determine the integral use integration by substitution with

    u = 3x+4 which will give \frac{du}{dx}=3

    After some simplifications you should come out with V=\frac{\pi}{20}

    to b) Are you asked to calculate the area between the x-axis and the graph of the function or do you want to evaluate the integral.

    In the first case you have to split the domain into 3 parts.
    In the second case you have to split the domain into 2 parts.

    Draw a sketch of the graph and you'll see why these preparations are necessary.
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