<p>ok, its volume generated when the solid is revolved around stuff.</p>
<p>so, when its revolved about the x-axis or modification:</p>
<p>about y=a
its integral of a-f(x)
about y=-a
its integral of a+f(x)</p>
<p>ABOUT y-axis; using shells</p>
<p>about x=a
integral of (a-x)<em>f(x)
about x=-a
integral of (a+x)</em>f(x)</p>
<p>thanks a lot guys!!!</p>
<p>Remember that the integrand of your solid of revolution formula (washer method) would be
f(x)^2 - g(x)^2</p>
<p>Where f(x) is your outside curve, and g(x) is your inside curve. In the case of revolving about a line parallel to the x axis, g(x)=constant= a. Also, f(x) > g(x) for all x between the bounds of your definite integral. </p>
<p>So I suppose it depends whether y=a is above or below f(x). If it is below f(x) then the integrand should be f(x)^2 - a^2. (Someone else check my logic :-p)</p>
<p>nevermind I figured it out:</p>
<p>here's the whole shebang:</p>
<p>washers: about x-axis or horizontal lines:</p>
<p>about y=a (if a is ab above f and g)
v = pi * Integral ((a-BOTTOM graph)^2 - (a-TOP graph)^2)</p>
<p>about y=-a (if a is below f and g)
v = pi * Integral ((a + TOP graph)^2 - (a + BOTTOM graph)^2)</p>
<p>DISK METHOD: same as above BUT for y=a USE (a-TOP)^2 -(a-BOTTOM)^2 INSTEAD of bottom - top</p>
<p>SHELLS: about y-axis, and vertical lines:</p>
<p>x=a
v= 2pi * Integral ( (a-x)(top - bottom))</p>
<p>x=-a
v = 2pi * Integral( (a+x) * (top-bottom) )</p>
<p>THESE ARE ALL CORRECT; I HAVE TESTED THEM HEAVILY, BY USING THEM TO SOLVE QUESTION IN MY TEXT AND BARRONS AP GUIDE 2008 :)</p>