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

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The discussion revolves around finding the volume of a solid formed by rotating the function y=|sin(2x)*cos(2x)| around the line y=0. Participants confirm that the integral setup appears correct, noting that the function is zero at x=π/4. The correct integration limits are clarified to be from 0 to π, rather than 0 to π/2. The final volume calculated for the solid is V=(π^2)/8. This highlights the importance of accurate limits in volume calculations for rotational solids.
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
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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