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 and Answers Forum

All Questions Topic List
Relation and Functions Questions
Previous in All Question Next in All Question
Previous in Relation and Functions Next in Relation and Functions
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

$t h a n k s s i r m j s .$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum