Evaluate the following \[ \int_{0}^{9} f(x) d x, \text { where } f(...

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Evaluate the following
\[
\int_{0}^{9} f(x) d x, \text { where } f(x)=\left\{\begin{array}{ll}
\sin x & \text { if } 0 \leq x \leq \frac{\pi}{2} \\
1 & \text { if } \frac{\pi}{2} \leq x \leq 3 \\
e^{x-3} & \text { if } 3 \leq x \leq 9 .
\end{array}\right.
\]
\( \mathrm{P} \)
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