calculus proof: Suppose that f is integrable on [a,b] and 0 < m ≤ f(x) ≤M for all x in the interval [a,b].?
Prove that :
a) m(a-b) ≤ ∫ from a to b of f(x)dx ≤ M (b-a)
b) Use this result to bound ∫ from 0 to 1 of √(1+x^4 ) dx
Update:Thanks, I understand it more now!
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Integrate your given inequality!
(I think you have a typo, by the way)
The integral of the constant m, from a to b, is mx[x = a; x = b] = mb - ma = m(b - a).
The same goes for M.
Now we need to find upper and lower bounds for √(1 + x^4) on the interval [0, 1].
Notice that f(0) = 1 and f(1) = √(2)
Can you take it from here?