Examples 7.1.13(c):

If f is an integrable function defined on [a, b], which is bounded by M on that interval, prove that
M (a - b) f(x) dx M (b - a)
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Since f is bounded on [a, b] by M we know that
-M f M
Therefore:
-M dx f(x) dx M dx
or equivalently (we have computed the left and right integrals before):
-M (b - a) f(x) dx M (b - a)

Interactive Real Analysis, ver. 1.9.5
(c) 1994-2007, Bert G. Wachsmuth
Page last modified: Mar 28, 2007