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use cylindrical shells method to find the volume of the solid generated when the region...
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High School Teacher
The formula for calculating the volume of a solid rotating about `y`-axis is
In your case `f(x)=2cos(9x^2)` `a=0,b=sqrt(pi)/6`
hence we have
`V=2piint_0^(sqrt pi/6)x cdot 2cos(9x^2)dx=|(t=9x^2),(dt=18xdx),(a_t=0),(b_t=pi/4)|=`
` ` ` ` `(2pi)/9int_0^(pi/4)costdt=(2pi)/9sint |_0^(pi/4)=(2pi)/9(sqrt2/2-0)=(sqrt2pi)/9`
Hence the volume of your rotating solid is `(sqrt2 pi)/9`
Posted by tiburtius on September 21, 2013 at 6:48 AM (Answer #1)
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