(7) The area of the region enclosed by the graph of the function $y=1+\cos x, x \in[-\pi, \pi]$ and the $x$-axis is $\qquad$ .
(7) $2 \pi$ Hint: Draw four lines $y=2, x=-\pi, x=\pi, y=0$, then the graph of the given function lies within the rectangle formed by these four lines, and is symmetric about the $y$-axis. The part in the first quadrant, the graph of the function is centrally symmetric about the point $\left(\frac{\pi}{2}, 1\right)$, so the area enclosed by this part of the function graph, the $x$-axis, and the $y$-axis, is equal to half the area of the corresponding rectangle. Therefore, the area enclosed by the entire function graph and the $x$-axis is half of the area of the aforementioned rectangle, which is $2 \pi$.