140.sagews

# 15.2 #28
# ---------

# I've drawn the solid that you're asked to find the volume of in this problem.

var('x,y')
f = 1 + exp(x)*sin(y)
bottom = sage.plot.plot.polygon([[-1,pi],[1,pi],[1,0],[-1,0]],rgbcolor=(.5,.5,1))
sides = parametric_plot3d([-1,y,x*f(-1,y)],(x,0,1),(y,0,pi)) +\
    parametric_plot3d([1,y,x*f(1,y)],(x,0,1),(y,0,pi)) +\
    parametric_plot3d([x,0,y*f(x,0)],(x,-1,1),(y,0,1)) +\
    parametric_plot3d([x,pi,y*f(x,pi)],(x,-1,1),(y,0,1))
top = plot3d(f,(x,-1,1),(y,0,pi))

top + bottom + sides