If you don't do 4u this will mean nothing to you.
I only just realised how to tell whether to use shells or slices in a particular situation.
Keeping in mind that the main idea behind slices is integrate(pi(R^2-r^2))dy, where R and r will be either constant or in terms of x, it stands to reason that the inverse of the function (or to be precise, finding x in terms of y) should be relatively easy to find then integrate.
Similarly, the main idea behind shells is int.(2*pi*x*y)dx, if you quickly multiply your function by x in your head and it's still integrate-able, then you're all good. Luckily just about every expression in x is still integrate-able if you multiply it by x, it's just that sometimes the slices may actually be simpler.
I can't be bothered listing examples where slices would be better than shells because you're all 4u kids and you're smart enough to work it out yourself :P
2 comments:
I have a question! How do you study for 4u math and 3u math, sorry for the anon status!
I just did past papers for my y12 exams.
I kinda slacked off for T4 and T1, especially for 4u, and it showed :L
My massive jump from year 10 to year 11 was because I made notes to the maths syllabus (yes it exists) to make sure I had all my fundamentals down. I may do that again for trials, but definitely before HSC.
If you can't be bothered doing that - just every paper that you do is doing you good.
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