Write and evaluate the definite integral that represents the volume of the solid formed by revolving the region about the y-axis. y = V 49 - x2 6- 5- y 4- 3 2 1- 3 4

Suppose that r=12 cm and h=15 cm in the right circular cylinder. Find the exact and approximate a lateral area. b total area. c volume.

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.

Find the volume of the solid obtained by rotating the region enclosed by the curves y = 32 x2 y = 2 +1– x²| about - y = 25. (Use symbolic notation and fractions where needed.) Volume =| %3D