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Kruka [31]
4 years ago
9

The region bounded by y=5/x, y=0, x=1, and x=3 is rotated about the x-axis. find the volume of the resulting solid.

Mathematics
1 answer:
brilliants [131]4 years ago
6 0
Volume of Revolution  = \pi  \int\limits^b_a {y^{2}} \, dx
Volume of Revolution  = \pi \int\limits^3_1 { (\frac{5}{x})^{2}} \, dx
= \pi \int\limits^3_1 ({\frac{25}{x^{2}}) \, dx
= 25\pi \int\limits^3_1 ({\frac{1}{x^{2}}) \, dx
= 25\pi \int\limits^3_1 ({x^{-2}}) \, dx
= 25\pi \ ^{3} [-x^{-1}] _{1} 

= 25\pi\ ((-1/3) - (-1/1)) \\
= 25\pi\ (2/3) \\
= 50/3 \pi\ units^{3}
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