K=1 gle around 10. lim [ 27 ( * 2 ) 312 ( # ) , with * * = " gle around K = 1 Each of the definite integrals in Exercises 11-16 represents escribed in the volume of a solid of revolution obtained by rotating a re- erent than gion around either the x- or y-axis, computed with the shell method. Find this region. IT / 4 se volume 11. 2nt x cos x dx 12. 2x x(x2) dx ot shells. se volume washers. 13. 2nt yay - 4 dy 14. 27 (x2 -x3) dx J4 computed 15. 27 ylnydy 16. 2x (3y - 3y2 ) dy y = 4 on the geo- Write the volumes of the solids of revolution shown in around Exercises 17-20 in terms of definite integrals that represent accumulations of shells. Do not solve the integrals. 17. 18. 2+ y = f (x) r = 3 on y = f ( x ) the geo- around 2 X 2 3 -1- 1 -2- are they -2 19. e x-axis y y = f(x ) 20. y approx- N int sum y = f (x ) ann sum kimation und the X the solid -1 and the -2 e region