# calculus

posted by .

2. Let R be the region of the first quadrant bounded by the x-axis and the cuve y=2X-X^2
a. Find the volume produced when R is revolved around the x-axis
b. Find the volume produced when R is revolved around the y-axis

• calculus -

the x-intercepts are 0 and 2
a) Vol = π ∫ (2x-x^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 + √(4-4y) - (2 - √(4-4y))
= 2√(4-4y)
so radius^2 = 4(4-4y) = 16 - 16y

volume = π∫(16-16y) dy from 0 to 1 , (the max height of the parabola is 1)

again , the rest is easy.

## Similar Questions

1. ### 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 y-axis ?
2. ### 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.
3. ### calculus

Let A be the region bounded by the curves y=x^2-6x+8 and y=0, find the volume when A is revolved around the x-axis
4. ### Calculus

Let A be the region bounded by the curves y = x^2-6x + 8 and y = 0. Find the volume obtained when A is revolved around the Y-AXIS
5. ### Calculus

Let A be the region bounded by the curves y = x^2-6x + 8 and y = 0. Find the volume obtained when A is revolved around the Y-AXIS
6. ### calculus

let R be the region of the first quadrant bounded by the x-axis and the curve y=2x-x^2. Find the volume produced when R is revolved around the X-axis
7. ### AP Calculus

Let R be the region bounded by the x-axis and the graph of y=6x-x^2 Find the volume of the solid generated when R is revolved around the y-axis
8. ### 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 x-y =2
9. ### CALCULUS HELP PLZ

The region R is bounded by the x-axis, y-axis, 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 x-axis. C. The solid formed in part B is divided …
10. ### CALCULUS

The region R is bounded by the x-axis, y-axis, 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 x-axis. C. The solid formed in part B is divided …

More Similar Questions