Prove that [latex]\int_{t-T / 2}^{\overline{t+T / 2} \phi d \xi}=\int_{t-T / 2}^{t+T / 2} \bar{\phi} d \xi[/latex] where f is Φ constinuous function of [latex]\xi[/latex]

[latex]\int_{t-T / 2}^{\overline{t+T / 2} \phi d \xi}=\frac{1}{T} \int_{t-T / 2}^{t+T / 2}\left[\int_{t-T / 2}^{t+T / 2} \phi d \xi\right] d t[/latex] Changing the order of integration, we can write or [latex]\int_{t-T / 2}^{\overline{t+T / 2} \phi d \xi}=\int_{t-T / 2}^{t+T / 2} \frac{1}{T}\left[\int_{t-T / 2}^{t+T / 2} \phi d t\right] d \xi[/latex] or [latex]\int_{t-T / 2}^{\overline{t+T / 2} \phi d \xi}=\int_{t-T / 2}^{t+T / 2} \bar{\phi} d \xi[/latex]

Question 10.1: Prove that where f is Φ constinuous function of ζ

Introduction to Fluid Mechanics and Fluid Machines

Prove that

\int_{t-T / 2}^{\overline{t+T / 2} \phi d \xi}=\int_{t-T / 2}^{t+T / 2} \bar{\phi} d \xi

where f is Φ constinuous function of $\xi$

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