Suppose that $f$ and $g$ are integrable on $[a, b]$, then $f+g$ is integrable on ......... .

Question

Aicharya · Accepted Answer

As $f$ and $g$ are integrable on $[a, b]$, then $\int_{x_1}^{x_2} f(x) d x$ and $\int_{x_1}^{x_2} g(x) d x$ exists for every value of $x_1, x_2 \in[a, b]$, then $\int_{x_1}^{x_2} f(x) d x+\int_{x_1}^{x_2} g(x) d x=\int_{x_1}^{x_2}(f+g)(x) d x$ Also exists for $\forall x_1, x_2 \in[a, b]$ Hence, option (c) is correct.

Suppose that \(f\) and \(g\) are integrable on \([a, b]\), then \(f+g\) is integrable on ......... .

Solution