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

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SUMMARY

The discussion focuses on calculating the volume of the solid formed by rotating the function y=|sin(2x)*cos(2x)| around the line y=0. The correct integral for this volume is determined to be from 0 to π, leading to a final volume of V=(π^2)/8. The participants confirm the integral's correctness and clarify the limits of integration, emphasizing the importance of accurately defining the bounds for proper volume calculation.

PREREQUISITES
  • Understanding of integral calculus
  • Familiarity with the concept of volume of revolution
  • Knowledge of trigonometric functions, specifically sine and cosine
  • Ability to interpret and analyze graphical functions
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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
 

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