Question

If ${\int }_a^{b}f\left(t\right)goh\left(t\right)={\int }_a^{b}foh\left(t\right)g\left(t\right)d\left(t\right)$, where $f,g,h,$ are non negative continuous functions on $[a,b]$ then possible choice of $h\left(t\right)$ is

• A. $t$
• B. $a-b-t$
• C. $a+b-t$
• D. $b-t$

Answer 1

Answer: (A), (C)

$t$
$a+b-t$

Equality in true if $f\left(t\right)goh\left(t\right)=foh\left(t\right)g\left(t\right)$
or $f\left(t\right)goh\left(t\right)=foh(a+b-t)g(a+b-t)$