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Question Number 153918 by joki last updated on 12/Sep/21
the base of an object is in the form of a circle with  radius 1. suppose that all section of the object are  perpendicular to a diameter of a square. determine  the volume of the object?
thebaseofanobjectisintheformofacirclewithradius1.supposethatallsectionoftheobjectareperpendiculartoadiameterofasquare.determinethevolumeoftheobject?
Answered by talminator2856791 last updated on 12/Sep/21
       ≡ 2∫_0 ^( (π/2))  (2∙sin(x))^2 dx            = 2π
20π2(2sin(x))2dx=2π
Commented by alisiao last updated on 12/Sep/21
=  (2 ∫_0 ^( (𝛑/2)) ( ((e^(ix) −e^(−ix) )/i))^2 dx)    =(−2 ∫_0 ^( (𝛑/2)) ( e^(2ix)  −2 +e^(−2ix) )dx)    =  (−2 ((e^(2ix) /(2i)) − 2x − (e^(−2ix) /(2i)))_( 0) ^( (𝛑/2))  )    =(−2( sin(2x) −2 x)_( 0) ^( (𝛑/2)) )    =  [ −2(0−𝛑)] = 2𝛑    ⟨ M . T  ⟩
=(20π2(eixeixi)2dx)=(20π2(e2ix2+e2ix)dx)Missing \left or extra \rightMissing \left or extra \right=[2(0π)]=2πM.T
Commented by alisiao last updated on 12/Sep/21
= 8 ∫_0 ^( (𝛑/2))  sin^2 (x) dx = 8 ∫_0 ^( (𝛑/2)) (1/2)(1−cos(2x))dx    = 4 ( x − (1/2)sin(2x))_0 ^( (𝛑/2)) = 4 ( (𝛑/2) ) = 2𝛑    ⟨ M . T  ⟩
=80π2sin2(x)dx=80π212(1cos(2x))dx=4(x12sin(2x))0π2=4(π2)=2πM.T

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