Chapter 8.3, Problem 35E

Find the volumes of the solids generated by revolving the regions bounded by the graphs of the equations about the given lines. y = x? y = 6x – x2 (a) the x-axis (b) the line y = 10

solve

Q3 b)

2

Find the valume of the solid generated by revolving the region bounded by y= -2x2 and y= x2 - 3, in the 4th quadrant about the : the line x =-1 the line y =4

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.