*wherever the variables a or b are mentioned, they refer to the integral existance theorem, where 'If f is continuous on [a,b], then f is integrable on [a,b]'.
*dark blue text represents the equation or theorem, dark red represents notes in the midst.
The directions are:
Find the volume of the solid that is generated by rotating around the indicated axis the plane region bounded by the given curves.
Indeed. The problem:
y=x^2, y=0, x=1; the x-axis
So that's all I get to work with. And I'm not doing such a fine job of finding the volume of the solid. If it helps at all, the central theorem of the lesson was "The Definition of Volume by Cross Sections":
If the solid R lies alongside the interval [a,b] on the x-axis and has continuous cross sectional area function A(x), then its volume V=v(R) is V=∫ (where 'b' and 'a' remain in variable form) A(x) dx.
Any thoughts? o0
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