- #1

xwolfhunter

- 47

- 0

Secondly, I wanted to integrate a three-dimensional object that was not a two-dimensional function spun around its axis. So I thought up two functions,

[itex]y=x^2[/itex] if [itex]y≤4[/itex]

[itex]z=-y^2+16[/itex]

because they work well together, and the shape they produced (according to how I thought they'd do it) was good.

So, the way I thought I'd determine the volume was this,

[tex]V=\int_0^4 (-y^2+16)\,dy*\int_0^2 x^2\,dx[/tex]

which results in [itex]17\frac{2}{3}[/itex].

Then I tried to split the volume into four equal parts along the z-axis, but I messed up somewhere (though if I'm right about the volume I'm right about my method, I know this) and haven't finished the calculations.

So if you could let me know if I'm doing this right, I'd appreciate it, and if I'm doing it wrong, please tell me how to do it right.

Thanks!