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March 21st, 2019, 10:20 AM  #1 
Member Joined: Feb 2018 From: Iran Posts: 52 Thanks: 3  Application if integral
Find the volume of the solid figure generated by rotating the area of region bounded by y=4x1 and the xaxis on [0,3] about y_axis

March 21st, 2019, 12:02 PM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 3,016 Thanks: 1600  
March 21st, 2019, 12:48 PM  #3  
Member Joined: Feb 2018 From: Iran Posts: 52 Thanks: 3  Quote:
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.  
March 21st, 2019, 01:12 PM  #4 
Math Team Joined: Jul 2011 From: Texas Posts: 3,016 Thanks: 1600 
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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