<p>My teacher gave us a problem that read as:</p>
<p>There is a graph bounded by the first quadrant that has f(x) as 3x and g(x) as x^2. We than had to find its area which I used (3x - x^2) from 0 to 3 as that was where they intersected at and got 4.5. Does that seem right so far? The other questions were:</p>
<p>Find its volume rotated around the x-axis
Find its volume rotated around the y-axis
Find its cross section perpendicular to the axis</p>
<p>For the area I got 4.5, and for the other three I got bigger numbers which was why I had questioning for this problem. Just to clarify for the x-axis one I got around 37.5 and for the other two something like 8.1 and something else. Can anyone try this problem out and tell me what they get? Thanks :D.</p>
<p>Rotated around the x-axis, set up a disc method integral.</p>
<p>pi∫(3x)^2 - (x^2)^2 dx on [0,3] should equal around 101.788</p>
<p>Rotated around the y-axis, you can set up a disc method integral, but I’m lazy and will do the shell method.</p>
<p>2pi∫x(3x - x^2) dx on [0,3] should equal around 42.414</p>
<p>For the cross-section integral, you’re going to have to tell us what shape the cross-section is and what axis it’s perpendicular to.</p>
<p>For the y-axis though, shouldn’t it be using a different value than 3 since that is the x value? I think I used 9 for the y-value. And ah thanks that is what I forgot! To use pi in front.</p>
<p>Keasbey used the shell method for the y-value one, so it’s measured by the x-axis still. For discs you would have to change it.</p>
<p>Ah I see. Thanks alot :). Oh and it was perpendicular to the x-axis for the cross section question and its a bread slice.</p>