If \(f\) is integrable on \([0, a]\), then the function \(h\) defined on \([0, a]\) as \(h(x)=\ldots . .…

If \(f\) is integrable on \([0, a]\), then the function \(h\) defined on \([0, a]\) as \(h(x)=\ldots . . \forall x \in[0, a]\) is integrable on \([0, a]\)
  1. \(f(a-x)\)
  2. \(f(x-a)\)
  3. \(f(x)\)
  4. \(f(a)\)

Solution

Given, \(f\) is integrable an \([0, a]\) \(\begin{aligned} \therefore \quad h(x) & =\int_0^a f(x) d x \\ h(x) & =\int_0^a f(a-x) d x \end{aligned}\) Hence, option (a) is correct.

Asked in: AP EAMCET 2020 (18 Sep Shift 2)

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