Calculus

Q Consider the region enclosed by the curve g(x)=e^x and f(x)=0 for x ∈ [0,1]. Sketch a picture of this region, and then find the volume of solid obtained by rotating this region about the x axis using the slicing method. Also, describe in a short paragraph the shape of this solid.

Sketch the region enclosed by y=x and 4x+y^2-12=0, and if there are points of intersection, find them. As well  find the area of enclosed region using 1) a definite integral in terms of y and 2) a definite integral in terms of x.