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March 21st, 2019, 10:20 AM   #1
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Unhappy Application if integral

Find the volume of the solid figure generated by rotating the area of region bounded by y=4x-1 and the x-axis on [0,3] about y_axis
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March 21st, 2019, 12:02 PM   #2
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Find the volume of the solid figure generated by rotating the area of region bounded by y=4x-1 and the x-axis on [0,3] about y_axis
using the method of cylindrical shells ...

$\displaystyle V = 2\pi \int_0^3 x\left(4x-1 \right) \, dx$
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March 21st, 2019, 12:48 PM   #3
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using the method of cylindrical shells ...

$\displaystyle V = 2\pi \int_0^3 x\left(4x-1 \right) \, dx$
I only know one method which is this formula
Pi integral(a to b) (f(x)^2) can you explain in term of this formula ?
I tried solving it like this pi integral(-1to11)((y+1)/4)^2
Is it wrong cause it doesnt give the answer in my book

Last edited by Elize; March 21st, 2019 at 12:56 PM.
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March 21st, 2019, 01:12 PM   #4
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from y = -1 to y = 0, method of disks

from y = 0 to y = 11, method of washers


$\displaystyle V = \pi \int_{-1}^0 \left(\dfrac{y+1}{4}\right)^2 \, dy + \pi \int_0^{11} 3^2 - \left(\dfrac{y+1}{4}\right)^2 \, dy$

I recommend you learn the method of cylindrical shells ... makes problems like this rather simple.
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