Posted by Taeyeon on Friday, March 9, 2012 at 12:45pm.
2. Let R be the region of the first quadrant bounded by the xaxis and the cuve y=2XX^2
a. Find the volume produced when R is revolved around the xaxis
b. Find the volume produced when R is revolved around the yaxis

calculus  Reiny, Friday, March 9, 2012 at 1:00pm
the xintercepts are 0 and 2
a) Vol = π ∫ (2xx^2)^2 dx from 0 to 2
= π∫(4x^2  4x^3 + x^4) dx from 0 to 2
the rest is straighforward
b) this is is a little harder.
Solve the function for x
x^2  2x + y = 0
x = (2 ± √(4  4y) )/2
so the radius = 2 + √(44y)  (2  √(44y))
= 2√(44y)
so radius^2 = 4(44y) = 16  16y
volume = π∫(1616y) dy from 0 to 1 , (the max height of the parabola is 1)
again , the rest is easy.
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