That's what I intended. I'm not getting into specifics here... for sanity's sake. That stuff you can learn on your own.Originally posted by Silvercord
ygf I think I understand everything you've said in at least the broadest terms.
Yep.Are integrals used to find the area/volume of any weird forumla
Yep. Instead of adding up rectangles, you add up very flat discs. Or squares. Or what-have-you.(even graphed in 3d?).
Sometimes. But think about this:It seems that integrals are only an approximation.
f(t) = t + 3
The slope of that line, it's derivative, is 1.
f'(t) = 1
f'(t) just means the derivative of f(t)
Say I wanted to find out the area under f'(t) from t=0 to t=3. Since the integral is the area under the curve, and the integral is opposite the derivative:
f(t) is the integral of f'(t)
f(3) - f(0) = 6 - 3 = 3
That's exact. No approximation there. For polynomials you often don't need approximations because some formula will give you the exact answer. Sometimes you need to approximate because there is no other way. (Logs are approximations.)