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
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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