Question

In Exercises \(7-12,\) evaluate the integral. $$\int_{-4}^{-1} \frac{\pi}{2} d \theta$$

Short answer

The value of the integral \(\int_{-4}^{-1} \frac{\pi}{2} d \theta\) is \(\frac{3\pi}{2}\)

Step-by-step solution

Identify the function and boundaries

The function to integrate is \(\frac{\pi}{2}\), which is a constant function. The boundaries for the integral are -4 and -1. Therefore, the integral to compute is \(\int_{-4}^{-1} \frac{\pi}{2} d \theta\).

Compute the integral of the constant function

Since the function is a constant, we can factor it out of the integral and multiply it by the difference between the upper and lower bounds of the integral. It gives us \(\frac{\pi}{2} × [-1 - (-4)] = \frac{3\pi}{2}\).

Conclusion

Therefore, the integral of \(\frac{\pi}{2}\) from -4 to -1 is \(\frac{3\pi}{2}\).