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March 22nd, 2019, 08:39 AM   #1
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Exclamation Finding volume of solid formation using disck method

find the volume of the solid figure generated by rotating the area of the region bounded y=1/x the x axis x=1 and x=3 about y_axis
How to solve this question using ring methode? I've added my way of solving the question but I am not sure if its true if it's not can you please say where I did wrong?

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March 22nd, 2019, 08:50 AM   #2
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two integrals are required ...

$\displaystyle V = \pi \int_0^{1/3} 3^2 - 1^2 \, dy + \pi \int_{1/3}^1 \left(\dfrac{1}{y}\right)^2 - 1^2 \, dy$

one integral using cylindrical shells ...

$\displaystyle V = 2\pi \int_1^3 x\left(\dfrac{1}{x}\right) \, dx$
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