The velocity function (in meters per second) is given for a particle moving along a line.

v(t) = t² 2t 15, 1 t 6

(a) Find the displacement of the particle for the given time interval. m (b) Find the distance traveled by the particle during the given time interval. m

Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the x-axis.

x = 3y² + 15y 18, x = 0