Question

Evaluate the definite integral: \[ \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} (\sin |x| + \cos |x|)_~dx \]

Hint:

An alternative way to think about this is that the graph of \(\sin|x| + \cos|x|\) is identical on both the left and right sides of the y-axis. You can just calculate the area for the right side (\(x > 0\)) and multiply it by 2.

Answer 1