Chapter 9, Problem 54RE

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x°, y = 1, x = 2; about y = -5 V = Sketch the region. y y 4 Sketch the solid and a typical disk or washer. Graph Graph Description Graph Graph Description Graph Graph Description Graph Graph Description 15- -2 --15 -15 ol

Use any method to find the volume, V, of the solid obtained by rotating the region enclosed by the curves about the given axis. y² = x¯¹, x = 1, (Express numbers in exact form. Use symbolic notation and fractions where needed.) X = 6, axis y = −6 V = (156+24√√6 +ln(6))π Incorrect < Feedback You have not correctly calculated the volume of the solid. Slice the region vertically and use the washer method to find the volume of the solid of revolution. b [*(Router - Riner) dx a V = π X Note that a and b are the x-coordinates of the intersection points. Find Router as the distance from the axis of rotation to the top point of the region. Find Rinner as the distance from the axis of rotation to the bottom point of the region.

y = 4-x The volume of the solid generated when the shaded region shown above is rotated through a complete revolution about the y- axis is Select one: anything DELL

Show graph and solve for its intersection points.  Solid of Revolution