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 crosssections of the solid perpendicular to the yaxis are squares. Find the volume of the solid.
(c) A solid has base R and the crosssections of the solid perpendicular to the yaxis 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 (1x^2) dx etc

Calculus  Jake, Thursday, January 28, 2010 at 6:45pm
What is symmetric around the yaxis? 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 xaxis? 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
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