anonymous
  • anonymous
Consider the following graph: http://i55.tinypic.com/288nvpz.gif a=4 and b=5 Refer to the figure and find the volume V generated by rotating the region R1 about the line AB.
Mathematics
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anonymous
  • anonymous
Consider the following graph: http://i55.tinypic.com/288nvpz.gif a=4 and b=5 Refer to the figure and find the volume V generated by rotating the region R1 about the line AB.
Mathematics
chestercat
  • chestercat
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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dumbcow
  • dumbcow
R1 is region bounded by y = 4x^5, y=0, and x=1 Rotating around vertical axis x=1 means we will look at horizontal cross-sections which are circular with radius that is x-distance from 4x^5 and x=1 Also we will integrate w/ respect to y since each horizontal cross-section has height of dy get x in terms of y y=4x^5 --> x = (y/4)^1/5 radius = 1 - (y/4)^1/5 V = pi*integral 0-4 R^2 dy R^2 = (1-(y/4)^1/5)^2 = 1-2(y/4)^1/5 +(y/4)^2/5 \[V = \pi \int\limits_{0}^{4}(y/4)^{2/5} -2(y/4)^{1/5}+1 dy\] u=y/4 ---> du =dy/4 -->4du = dy \[V = 4\pi \int\limits_{0}^{4}u ^{2/5} - 2u ^{1/5}+1 du \] \[V=4\pi |_{0}^{4} \left( 5/7(y/4) ^{7/5}- 5/3(y/4) ^{6/5} +y/4 \right)\] \[V =4\pi/21\]

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