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    Integrals, Area under the Curve and Solid of Revolution

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    1.
    Evaluate:
    ∫2cos2 xdx

    2.
    Figure 12.1
    y = 9-x2 , y=5-3x

    Sketch the region bounded by the graphs of Figure 12.1, and
    then find its area.
    3.
    Figure 13.1
    1?0x4dx

    Approximate the integral (Figure 13.1); n=6, by:
    a) first applying Simpsonfs Rule and
    b) then applying the trapezoidal rule.
    4.
    Find the mass M (in grams) of a rod coinciding with the interval [0, 4]
    which has the density function
    (x)= 5 sin 
    ________________________________________4 x

    5.
    The region R is bounded by the graphs
    x-2y=3 and x=y2
    Set up(but do not evaluate) the integral that gives the volume of the solid
    obtained by rotating R around the line x = -1.

    6.
    Figure 16.1
    y=2x2

    Find the volume of the solid that is generated by rotating the region
    formed by the graphs of Figure 16.1 and y = 4x about the line x = 3.
    7.
    Use the method of cylindrical shells to find the volume of the solid
    rotated about the line x = -1 given the conditions:
    y = x3 - x2; y = 0; x = 0

    8.
    Find the length of the graph of
    y = 1
    ________________________________________3 x3/2 - x1/2
    from
    (1, - 2
    ________________________________________3 )
    to
    (4, 2
    ________________________________________3 )

    9.
    A 10-ft trough filled with water has a semicircular cross section of
    diameter 4 ft. How much work is done in pumping all the water over
    the edge of the trough? Assume that water weighs
    62.5lb/ft3

    10.
    Figure 20.1
    y = x2
    ________________________________________2

    The region in the first quadrant bounded by the graphs of y = x and Figure 20.1 is rotated around the line y = x. Find
    (a) the centroid of the region and
    (b) the volume of the solid of revolution.

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    https://brainmass.com/math/integrals/integrals-area-under-the-curve-and-solid-of-revolution-167047

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    Solution Summary

    Integrals, Area under the Curve and Solid of Revolution are investigated.

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