Posted by **Jake** on Thursday, January 28, 2010 at 2:36am.

R is the region in the plane bounded below by the curve y=x^2 and above by the line y=1.

(a) Set up and evaluate an integral that gives the area of R.

(b) A solid has base R and the cross-sections of the solid perpendicular to the y-axis are squares. Find the volume of the solid.

(c) A solid has base R and the cross-sections of the solid perpendicular to the y-axis are equilateral triangles. Find the volume of the solid.

- Calculus -
**Damon**, Thursday, January 28, 2010 at 2:46am
it is symmetric around the y axis so do the integral from x = 0 to x = 1 and double it

2 int from 0 to 1 of x^2 dx

2 (x^3)/3 = 2/3

length of side of square = 2x^2

area of cross section = 4 x^4

integrate 4 x^4 dx from 0 to 1

now do the same for area of cross section = x^4 sqrt 3

- whoops -
**Damon**, Thursday, January 28, 2010 at 2:54am
I did the area below the line. For between use (1-x^2) dx etc

- Calculus -
**Jake**, Thursday, January 28, 2010 at 6:45pm
What is symmetric around the y-axis? This is confusing because I don't really know how to draw the solid. First it says the solid has the base of R. So does that mean R should be on the x-axis? But how do you find out the length of the side of the square? Is one side of the square solid bounded by the region so that one of the sides of the square faces of the solid supposed to have a length that is from one intersection point of both curves to the other intersection point? Same goes for part c. Thanks

## Answer This Question

## Related Questions

- Calculus - R is the region in the plane bounded below by the curve y=x^2 and ...
- Calculus - R is the region in the plane bounded below by the curve y=x^2 and ...
- calculus - Set up, but do not evaluate, the integral which gives the volume when...
- math - The region R, is bounded by the graphs of x = 5/3 y and the curve C given...
- math - The region R, is bounded by the graphs of x = 5/3 y and the curve C given...
- MATH-HELP! - The region R, is bounded by the graphs of x = 5/3 y and the curve C...
- why won't anybody help me - The region R, is bounded by the graphs of x = 5/3 y ...
- calculus - 1. Find the area of the region bounded by f(x)=x^2 +6x+9 and g(x)=5(x...
- Calculus AB - Let R be the region bounded by the graphs of y=sin(pi x) and y=(x^...
- Calculus check - The functions f and g are given by f(x)=sqrt(x^3) and g(x)=16-...

More Related Questions