Pure 2 help -june 2004 q Watch

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enchan
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Hi got an exam on monday, im a bit stuck,

curve y=sq.root(3x+1)

region r is bound by the curve and lines, x=0, x=5, y=0

i) Show by integration that the exact area of R is 14.


ii) The region R is rotated thru 4 right angles about the x-axis. Find the exact volume of the solid formed.

Please help!! thanks!
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J.F.N
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(Original post by enchan)
Hi got an exam on monday, im a bit stuck,

curve y=sq.root(3x+1)

region r is bound by the curve and lines, x=0, x=5, y=0

i) Show by integration that the exact area of R is 14.


ii) The region R is rotated thru 4 right angles about the x-axis. Find the exact volume of the solid formed.

Please help!! thanks!
i. Let [ denote integral
(0 to 5)[sqrt(3x+1).dx
Use substitution u=3x+1 and integrate
so you get
(0 to 5)[sqrt(3x+1).dx = (2/9).(3x+1)^(3/2)=(2/9).(16)^(3/2) - 2/9 = 14
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Fermat
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ii)
Volume of rotation as you described it is given by,

V = π∫ y² dx, over the range x = 0 to x = 5

V = π∫ {0 -> 5} (3x + 1) dx
V = π (3x²/2 + x){0 -> 5}
V = π {(3*25/2 + 5) - (0 - 0)}
V = 42.5π
========
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