Define R as the region bounded by the graphs of f(x)=4x2 −4x+2, x=0, x=1, and the x-axis. Using the disk method, what is the volume of the solid of revolution generated by rotating R about the x-axis? Enter your answer in terms of π.

Suppose that a thin metal wire in the shape of a semicircle occupies the curve C, where C is the top half of the circle x² + y² = 9. The mass density of 2 6 the wire is described by the function p(x, y) = xy. Find the total mass of the wire.

Let the functions f (x) = (x - 5)? and g(x) = x² + x + 3. Determine an integral which makes it possible to calculate the volume of the solid of revolution (without calculating the integral) generated by the rotation of the surface S delimited by f(x), g(x) and the axis of y around: (a) of the x-axis (b) of the y axis (c) of the y axis = 3 You have to sketch the situation for each letter and sketch the solid.