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(A) If a function $f$ is integrable on $[0, a]$,then any function derived from it by a linear transformation of the variable,such as $f(a-x)$,is also

Vedclass · Accepted Answer

$f(a-x)$

Vedclass · Answer

(A) If a function $f$ is integrable on $[0, a]$,then any function derived from it by a linear transformation of the variable,such as $f(a-x)$,is also integrable on $[0, a]$.This is a standard property of Riemann integrable functions.Specifically,if $f$ is integrable on $[0, a]$,then the composition $f(a-x)$ is integrable on $[0, a]$ because the transformation $u = a-x$ is a continuous and monotonic mapping.Therefore,$f(a-x)$ is integrable on $[0, a]$.Thus,option $A$ is correct.

If $f$ is integrable on $[0, a]$,then the function $h$ defined on $[0, a]$ as $h(x) = \int_0^x f(t) dt$ is integrable on $[0, a]$. Which of the following functions is also integrable on $[0, a]$?

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