f-function-integrable-on-a-b-is-max-a-b-f-x-dx-a-b-maxf-x-dx-if-not-give-a-opposite-example-

Question Number 63389 by mathmax by abdo last updated on 03/Jul/19

f f u n c t i o n i n t e g r a b l e o n [a, b]

i s m a x \int_{a}^{b} f (x) d x = \int_{a}^{b} m a x f (x) d x ? i f n o t g i v e a o p p o s i t e e x a m p l e .

Commented by MJS last updated on 03/Jul/19

opposite example

\underset{a}{\int^{b}} (1 - x^{2}) d x = \frac{1}{3} (a^{3} - b^{3}) - (a - b)

\max (\frac{1}{3} (a^{3} - b^{3}) - (a - b)) = \frac{4}{3} with a = - 1 \land b = 1

\max (1 - x^{2}) = 1 with x = 0

\underset{- 1}{\int^{1}} 1 d x = 2

\frac{4}{3} \neq 2

Commented by mathmax by abdo last updated on 03/Jul/19

t h a n k s s i r m j s .