Find the volume of the solid formed by the rotation around the y=0

Michael_0039
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Homework Statement
Find the volume of the solid formed by the rotation around the y=0
y=|sin(2x)*cos(2x)|
Relevant Equations
nil
Hi,

I find this...
picpic.png


Please tell me your opinion on this.

Thanks.
 
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Michael_0039 said:
Homework Statement: Find the volume of the solid formed by the rotation around the y=0
y=|sin(2x)*cos(2x)|
Homework Equations: nil

Hi,

I find this...
View attachment 252926

Please tell me your opinion on this.

Thanks.
The integral itself looks right, although the graph of that function is zero at ##\pi/4##.

Did the question say to integrate from ##0## to ##\pi/2##?
 
PeroK said:
The integral itself looks right, although the graph of that function is zero at ##\pi/4##.

Did the question say to integrate from ##0## to ##\pi/2##?
Oops my mistake, it is: 0 ≤ x ≤ π

I have to fix it.

Thanks
 
So integrate from 0 to π: V=(π^2)/8
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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