7. The closed region in the first quadrant bounded by the curves y = x3 and y = 3
Ö x is rotated about the x-axis. What is the volume of the resulting solid?
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A. 1/2 |
B. 128 p /455 |
C. 16 p /35 |
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D. p /2 |
E. 32 p /35 |
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Solution: The answer is C
From the graph of
y = x3 and y = x1/3
We can see that the enclosed region is contained in the interval [0,1]. The volume (dV) created by rotating a vertical piece of thickness dx of the enclosed region about the x-axis is given by,
Thus, the total volume (V) can be found by integrating both sides of the above equation over the interval [0,1], as follows:
