Consider the region enclosed by the curves g(x) = ex and f (x) = 0 for x E [0, 1]. Sketch a picture...

Consider the region enclosed by the curves g(2)=e" and f(t) = 0 for re [0,1]. Sketch a picture of this region, and then find the volume of the solid obtained by rotating this region about the I-axis using the slicing method. Also, describe in a short paragraph the shape of this solid.