19) Evaluate the definite integrals: a) S sec20 tan30 de b) Sxvx+ 2 dx 20) Sketch the region enclosed by the given curves and find its area: y = 12 - x2, y =x2 -6 21) Find the volume of the solid obtained by rotating the region bounded the g about the specific line. Sketch the region, the solid, and a typical disk or wa a) y = =,y= 0x = 1x = 4 about the x - axis x b) x = 2 - y', x = y+, about the y - axis 22) Use the method of cylindrical shells to find the volume generated by rotat bounded by the given curves about the y-axis. y = 4x - x, y =x 23) Use the method of cylindrical shells to find the volume generated by rota bounded by the given curves about the x-axis. y = x3/2 , y = 8, x =0