my first 3-d problem, using integrals somehow. (calc 1)
So the problem is easy to understand, I think (I know what I'm supposed to find, I see what I'm being asked to do), but I have no idea of how to go about approaching this stuff. A little background. We're in the integrals chapter. We just learned the Substitution Rule (let u = whatever, du= whatever). A few days ago, we found the area between x^2 and x^3 on the interval [0,2], then we were asked to find the area between y^2 and y^3 on the same interval. Now we're being asked to imagine two portions of a parabola y=x^2 and y= -|x|^2 (is that right? the picture is definitely right.), formed into a flared conic-ish shape. The object is to find the volume of the pseudo-cone on the interval [0,1]. I can imagine the shape. I have no idea what to do. I don't know of any formulas for 3-d things. Integrals only find 'area' in 2-d, right? I've been sort of thinking about it in the back of my mind all day. . .can anyone point me in the right direction? Some days I feel completely out of my element in this class.
