find the volume of the solid generated when the region bounded by the y=x y=x+2, x=2 and x=4 revolved about the x-axis


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Question Number 141191 by Eric002 last updated on 17/May/21

$f i n d t h e v o l u m e o f t h e s o l i d g e n e r a t e d$ $w h e n t h e r e g i o n b o u n d e d b y t h e y = x$ $y = x + 2, x = 2 a n d x = 4 r e v o l v e d a b o u t t h e x - a x i s$
	Answered by ajfour last updated on 17/May/21
	$V=π∫_2 ^( 4) {(x+2)^2 −x^2 }dx =π(2x^2 +4x)∣_2 ^4 =π(24+8)= 32π$
	$V = π \int_{2}^{4} {{(x + 2)}^{2} - x^{2}} d x$ $= π (2 x^{2} + 4 x) ∣_{2}^{4}$ $= π (24 + 8) = 32 π$
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