Given

`y=cos(2x), y=0 x=0,x=pi/4`

so the solid of revolution about x-axis is given as

`V = pi * int _a ^b [R(x)^2 -r(x)^2] dx`

here

`R(x) =cos(2x)`

`r(x)=0` and the limits are `a=0 ` and` b=pi/4`

so ,

`V = pi * int _a ^b [R(x)^2 -r(x)^2] dx`

= `pi * int _0 ^(pi/4) [(cos(2x))^2 -0^2] dx`

=`pi * int _0 ^(pi/4) [(cos(2x))^2 ] dx`is the volume

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