1. Find the volume of the solid generated by rotating the region y = sin(3x), y = 0, x = 0, and x = ~ about the x- axis. 2. Use the shell method to find the volume generated by rotating the region bounded by the curves y = e2x y = 0, x = 0, and x = 1 about the y-axis. 3. Evaluate the integrals. a. (1 + x2 ) In ( 4x ) dx b. (2x + 3) sec2 x dx 4. Evaluate the integrals. . It/2 a. sin' x cost x dx b. csc5x cos'x dx 5. Evaluate the integral using trigonometric substitution. dx x2