# Question 8.T.6: (Linearity Property) If f1, f2 ∈ R(a, b) and k1, k2 ∈ R, the...

(Linearity Property)

If f_{1}, f_{2} ∈ \mathcal{R}(a, b) and k_{1}, k_{2} ∈ \mathbb{R}, then k_{1}f_{1} + k_{2}f_{2} ∈ \mathcal{R}(a, b) and

\int_{a}^{b}{k_{1}f_{1} + k_{2}f_{2}} = k_{1} \int_{a}^{b}{f_{1} + k_{2}} \int_{a}^{b}{f_{2}}.

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