Evaluate the integral.
$\int_{0}^{π} f (x) d x where f (x) = {\begin{cases} \sin (x) & if 0 \leq x < \frac{π}{2} \\ \cos (x) & if \frac{π}{2} \leq x \leq π \end{cases}$

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Final Answer: $0$

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Step 1 ：Given the function $f (x)$ which is defined as $\sin (x)$ for $0 \leq x < \frac{π}{2}$ and $\cos (x)$ for $\frac{π}{2} \leq x \leq π$ , we are asked to evaluate the integral of $f (x)$ from 0 to $π$ .

Step 2 ：We can split the integral into two parts, one for each condition of the function. The first integral will be from 0 to $\frac{π}{2}$ of $\sin (x)$ and the second integral will be from $\frac{π}{2}$ to $π$ of $\cos (x)$ .

Step 3 ：The integral of $\sin (x)$ from 0 to $\frac{π}{2}$ is 1.

Step 4 ：The integral of $\cos (x)$ from $\frac{π}{2}$ to $π$ is -1.

Step 5 ：Adding these two results together, we get a final integral of 0.

Step 6 ：Final Answer: $0$

Evaluate the integral.∫0πf(x)dx where f(x)={sin⁡(x) if 0≤x<π2cos⁡(x) if π2≤x≤π

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Evaluate the integral.
$\int_{0}^{π} f (x) d x where f (x) = {\begin{cases} \sin (x) & if 0 \leq x < \frac{π}{2} \\ \cos (x) & if \frac{π}{2} \leq x \leq π \end{cases}$