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    Finding volume bounded by given curves

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    18. Compute the volume of the solid formed by revolving the region bounded by about (a) the x-axis; (b) y = 4.

    20. Compute the volume of the solid formed by revolving the region bounded by and about (a) the y-axis; (b) x = 1.

    4. Sketch the region, draw in a typical shell, identify the radius and height of the shell, and compute the volume for the region bounded by and revolved about .

    6. Sketch the region, draw in a typical shell, identify the radius and height of the shell, and compute the volume for the region bounded by and , revolved about x = 2.

    8. Sketch the region, draw in a typical shell, identify the radius and height of the shell, and compute the volume for the region bounded by , revolved about y = 4.

    12. Use cylindrical shells to compute the volume of the region bounded by and x = 4, revolved about y = 2.

    14. Compute the arc length exactly.

    30. Set up the integral for the surface area of the surface of revolution, and approximate the integral with a numerical method.

    revolved about the x-axis

    36. Set up the integral for the surface area of the surface of revolution, and approximate the integral with a numerical method.

    revolved about the x-axis

    20. Evaluate the integral

    14. Evaluate the integral x dx

    Determine whether or not the integral is improper. If it is improper, explain why.
    (see attached)

    16. Find the indicated limit

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    18. Compute the volume of the solid formed by revolving the region bounded by about (a) the x-axis; (b) y = 4.

    (a)
    (b)

    20. Compute the volume of the solid formed by revolving the region bounded by and about (a) the y-axis; (b) x = 1.

    (a)
    (b)

    4. Sketch the region, draw in a typical shell, identify the radius and height of the shell, and compute the volume for the region bounded by and revolved about .

    The sketch is

    Since the part above x-axis is symmetry with the part below x-axis, we just consider the part ...

    Solution Summary

    The solution gives detailed steps on ten calculus questions: finding volume bounded by given curves using different methods, calculating arc length and surface area.

    $2.19

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