2011-10-27, 12:22 AM
As I said, solid volumes from revolution require a bit of imagination. Essentially, though, you only have 4 options: Disc method along the x-axis, Shell method along the x-axis, Disc method along the y-axis and Shell method along the y-axis.
If you can imagine what each thing does, every problem of that kind will be abreeze brawl, I guess. You have to juggle a lot of terms (most often fraction-polynomials which are a pain in the ass). I wouldn't associate the inability to copy numbers/terms from one line to another as incompatibility with Mathematics, though, you just need to pay more attention. If you STARE at that x^5 and write it down, it's not going to be 5x, likewise for -(-(-(-(x^-2/3)))).
At least that's what I do. I make careless stupid mistakes all the time, most of them being careless reading of the question (and thus answering a completely irrelevant question) or copying down the problem (like missing that tiny power of five above the sum). There are two things I do to make sure I don't do that on the exam: write EVERYTHING out (x^4 evaluated at (-2) is not 16, it is (-2)^4) and read EVERYTHING three times over (okay, here I substitute -2 in, I should get (-2)^4 here...-looks down- yep.)
Practice doing problems properly when you do homework/exercise. You get used to that (or the bad) style and you WILL use it on the exam, which is when you're under a lot more stress and prone to make a lot more errors.
If you can imagine what each thing does, every problem of that kind will be a
At least that's what I do. I make careless stupid mistakes all the time, most of them being careless reading of the question (and thus answering a completely irrelevant question) or copying down the problem (like missing that tiny power of five above the sum). There are two things I do to make sure I don't do that on the exam: write EVERYTHING out (x^4 evaluated at (-2) is not 16, it is (-2)^4) and read EVERYTHING three times over (okay, here I substitute -2 in, I should get (-2)^4 here...-looks down- yep.)
Practice doing problems properly when you do homework/exercise. You get used to that (or the bad) style and you WILL use it on the exam, which is when you're under a lot more stress and prone to make a lot more errors.