Suppose that f and g are integrable on [a, b] | vedclass

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(C) If $f$ and $g$ are integrable on the closed interval $[a, b]$,then by the linearity property of the definite integral,their sum $f+g$ is also inte

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$[a, b]$

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(C) If $f$ and $g$ are integrable on the closed interval $[a, b]$,then by the linearity property of the definite integral,their sum $f+g$ is also integrable on the same interval $[a, b]$.Specifically,for any $x_1, x_2 \in [a, b]$,the integrals $\int_{x_1}^{x_2} f(x) dx$ and $\int_{x_1}^{x_2} g(x) dx$ exist.Therefore,the integral of the sum is the sum of the integrals: $\int_{x_1}^{x_2} (f+g)(x) dx = \int_{x_1}^{x_2} f(x) dx + \int_{x_1}^{x_2} g(x) dx$.Since this holds for all $x_1, x_2 \in [a, b]$,$f+g$ is integrable on $[a, b]$.Thus,option $C$ is correct.

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

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