Posted by **Megan** on Sunday, April 1, 2007 at 11:31pm.

alright. i need to write a definite integral for the volume and evaluate the integral for the region bounded by y=x^2, y=0, and x=1 revolved about the a) x-axis, b) the y-axis, c) x=2, and d) y=-2.

HELP!

Lets do the x=2 axis.

dV= pi rh dr where r is radius, h is height. r= x-1 dr=dx h= y=x^2

dV= PI (x-1)x^2 dx

Then integrate from x=1 to 2

So the idea is to draw the pic, make an incremental dV in terms of r and h, change those to x,y variables.

What about rotating about y=6

dV= PI r h dr

r= 6-y y goes from 0 to 1^2

dr= dy

h= 1-sqrt(y)

check that picture

## Answer This Question

## Related Questions

- Calculus check - The functions f and g are given by f(x)=sqrt(x^3) and g(x)=16-...
- calculus - the region bounded by the graph f(x)=x(2-x) and the x axis is ...
- calculus - using the method of shells, set up, but dont evaluate the integral, ...
- MATH - Find the volumes of the solids generated by revolving the region in the ...
- Calculus check and help - Let R be the region bounded by the curves y=lnx^2 and ...
- Calculus AP - Let R be the region in the first quadrant bounded by the graph y=3...
- calculus - 8). Part 1 of 2: In the solid the base is a circle x^2+y^2=16 and the...
- Calculus - Find the volume of the solid whose base is the region in the xy-plane...
- calculus - 1. Find the area of the region bounded by f(x)=x^2 +6x+9 and g(x)=5(x...
- Calculus II/III - A. Find the integral of the following function. Integral of (x...

More Related Questions