- #1
Rectifier
Gold Member
- 313
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Hey!
It is the first time I post on this subform. Please forgive me if I do something wrong.
[tex]F(x)=\int^x_0f(t)dt[/tex]
for
[tex]R \in t \rightarrow f(t) [/tex]
Is it true that
[tex]0 \leq f(x)\leq 3[/tex] for [tex]0<x<1[/tex]
[tex]\int^x_0 tf(t)dt \leq x^2[/tex]
for all [tex]x \in (0, 1)[/tex]? "
[tex]\int^x_0 tf(t)dt \leq x^2 \Leftrightarrow t \int^x_0 f(t)dt \leq x^2 \Leftrightarrow t F(x) \leq x^2 [/tex]
I don't know how to continue from here.
It is the first time I post on this subform. Please forgive me if I do something wrong.
Homework Statement
[tex]F(x)=\int^x_0f(t)dt[/tex]
for
[tex]R \in t \rightarrow f(t) [/tex]
Homework Equations
Is it true that
[tex]0 \leq f(x)\leq 3[/tex] for [tex]0<x<1[/tex]
[tex]\int^x_0 tf(t)dt \leq x^2[/tex]
for all [tex]x \in (0, 1)[/tex]? "
The Attempt at a Solution
[tex]\int^x_0 tf(t)dt \leq x^2 \Leftrightarrow t \int^x_0 f(t)dt \leq x^2 \Leftrightarrow t F(x) \leq x^2 [/tex]
I don't know how to continue from here.
Last edited: