Using a graph, it can be shown that the approximate $x$-coordinates of the points of intersection of the two curves $y=3\sin(x^2)$ and $y=e^{x/2}+e^{-2x}$ are $x \approx 0.772$ and $x \approx 1.524.$ Use this information to approximate the volume of the solid obtained by rotating about the $x$-axis the region bounded by these curves.

Make sure your answer (based on the estimates given above) is correct to three decimal places.

Volume =