Posted by **Taeyeon** on Friday, March 9, 2012 at 12:45pm.

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 -
**Reiny**, Friday, March 9, 2012 at 1:00pm
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.

## Answer This Question

## Related Questions

- calculus - let R be the region of the first quadrant bounded by the x-axis and ...
- calculus - Let R be the region in the first quadrant bounded by the graphs of y=...
- AP Calculus - Let R be the region bounded by the x-axis and the graph of y=6x-x^...
- calculus - Let A be the region bounded by the curves y=x^2-6x+8 and y=0, find ...
- Calculus - Let A be the region bounded by the curves y = x^2-6x + 8 and y = 0. ...
- Calculus - Let A be the region bounded by the curves y = x^2-6x + 8 and y = 0. ...
- CALCULUS - The region R is bounded by the x-axis, y-axis, x = 3 and y = 1/(sqrt(...
- CALCULUS HELP PLZ - The region R is bounded by the x-axis, y-axis, x = 3 and y...
- MATH - Find the volumes of the solids generated by revolving the region in the ...
- calculus - Sketch the region R bounded by the graphs of the equations and find ...

More Related Questions