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Suppose f has absolute minimum value m and absolute maximum value M. Between what two values must the integral G lie?
I thought it was m(3) for abs min.
and M(3) for max. Is it 2 instead since 1-->3 is 2? Not sure. thanks for any help!
Suppose f has absolute minimum value m and absolute maximum value M. Between what two values must the integral G lie?
I thought it was m(3) for abs min.
and M(3) for max. Is it 2 instead since 1-->3 is 2? Not sure. thanks for any help!
What is a (Riemann) integral?
Let f be a function on [a,b] andbe a partition P of [a,b]. Let
where
is the minimum (actually greatest lower bound) of f on
. Similarly,
where
is the maximum of f on
The integralis that unique number with
for every partition P.
That's really the definition of integral. The great fundamental theorem of calculus allows "easy" computation of G.
In particular a partition with n=1, hasand
and so
So for your specific problem
All that is correct, but you should probably just remember the general rule that if a function has a bound,, then it's integral (if it exists) is bounded by M times the length of the interval,
. If you draw a graph and compare the two areas, it should be clear.
- Hollywood
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