calculus
posted by Taeyeon .
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

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.
Respond to this Question
Similar Questions

MATH
Find the volumes of the solids generated by revolving the region in the first quadrant bounded by the following about the given axes. x = y  y3, x = 1, y = 1 (b) Revolved about the yaxis ? 
calculus
Let R be the region in the first quadrant bounded by the graphs of y=e^x, y=1/2x+1, and x=2. Then find the volume of the solid when R is revolved about each of the following lines... the x axis, y=1, y=2, the y axis, x=1, and x=3. 
calculus
Let A be the region bounded by the curves y=x^26x+8 and y=0, find the volume when A is revolved around the xaxis 
Calculus
Let A be the region bounded by the curves y = x^26x + 8 and y = 0. Find the volume obtained when A is revolved around the YAXIS 
Calculus
Let A be the region bounded by the curves y = x^26x + 8 and y = 0. Find the volume obtained when A is revolved around the YAXIS 
calculus
let R be the region of the first quadrant bounded by the xaxis and the curve y=2xx^2. Find the volume produced when R is revolved around the Xaxis 
AP Calculus
Let R be the region bounded by the xaxis and the graph of y=6xx^2 Find the volume of the solid generated when R is revolved around the yaxis 
calculus
Sketch the region R bounded by the graphs of the equations and find the volume of the solid generated if R is revolved around the x axis. x= y^2 xy =2 
CALCULUS HELP PLZ
The region R is bounded by the xaxis, yaxis, x = 3 and y = 1/(sqrt(x+1)) A. Find the area of region R. B. Find the volume of the solid formed when the region R is revolved about the xaxis. C. The solid formed in part B is divided … 
CALCULUS
The region R is bounded by the xaxis, yaxis, x = 3 and y = 1/(sqrt(x+1)) A. Find the area of region R. B. Find the volume of the solid formed when the region R is revolved about the xaxis. C. The solid formed in part B is divided …