XAN E13. Find the integral expression for the volume. The region is bounded by; ! = Vx, y=0,x =4, revolve about y axis 4. Let R be the region in the first quadrant bounded by the graph of y = tanx , and the vertical line x = . Which of the following gives the volume of the solid generated when region R is revolved about the vertical line x = - ? A ) * 60 - arctany dy B) xx S' - tany dy y=et, yze"*,x =4, revolve about y axis C) x So - arctany dy D ) * So 16 - (arctany ) ? dy Let R be the resion bounded by the graph of y = Inx, y = 0, and I = e, Which of the 3 y = Vx, x=0,y= 4, revolve about x axis following gives the volume of the solid generated when region R is revolved about the line x = 1? A ) * Sol(e - 1) 2 - ( ny - 1) 2 ] dy B ) * So (ex - 1) 2 dy C ) * Sol(e - 1)2 - (ex - 1) 2 ] dy D ) * So [ ( 1 - e ) 2 - ( 1 + e " ) ? ) dy y= Vx-1, y =0,x=5, revolve about x = -1 3 6. Let R be the region bounded by the graph of y = x2 and y = 4x - x2 . Which of the following AP Style Problem . gives the volume of the solid generated when region R is revolved about the line y = 6? A ) # 2 2x2 - 4x dx 1. The region in the first quadrant bounded by y = \\9 - x2 , x = 0, and y = 0 is revolved about the x-axis. The volume of the solid generated is B ) x S 2 4x - 2x2 2 dx A) 97t C) * 50 | (2 2 -6)2 -(4x - 82 - 6 ) 2/ dx D) 72TC D ) # 50 (6 - 2 7 )2 - (6 - 4x+ 8 7) 2 / dx 2. The region in the bounded above by y = - x and x = y2 is rotated about the line y axis. The volume of the solid generated is A ) 647 14 7 . Let R be the region bounded by the graph of y= x and y = 4x - x . Which of the following B) 327 gives the volume of the solid generated when region R is revolved about the line x = 0? C) 64 7 15 A ) * Sox* - (4x -x7)2 dx 32 7 D) B) # 50 | 2# - (27 - 4x)2 / dx 15 C) 2x [ ' x (4x - x2) dx 3. The base of a solid is the region enclosed by the curve x2 + 4y? =4 . For the solid, each D ) 2x x ( 4x - 2x2) dx cross section perpendicular to the x-axis is a semicircle. What is the volume of the solid? A ) * 2 2 1 -2 dx 1QFind the volume of the solid whose base is the region bounded by the lines EXAN x+2y =6 . x =0, and y =0, if the cross sections taken perpendicular to the y axis are 10. Find the volume. Region bounded by y = x2, y = vx , revolve about x axis. rectangles of height 3. 2 Find the volume of the solid whose base is the region bounded by the lines Largest find the volume . Region bounded by y = x 7, y = Vix, revolve about y awl y= ~x, y=2x , and y = 4, if the cross sections taken perpendicular to the y axis are squares. 3. Find the integral expression for the volume. The region is bounded by y Find the integral expression for the volume. The region is bounded by; (x20) , y=0,x=2 and y= \\x, y=0,x=4, 2 y= \\x, x=0,y = 4, D revolve about x axis revolve about x axis revolve about y axis 2 revolve about y axis 3 y=et , y=0,x =0,x =2, y=e , y= 3, x=0, revolve about x axis revolve about y axis 3 revolve about line y = 5 4 revolve about line x = 3 y=x ( x20) y=4,x=0 6 y=x (x20), y=0,x=2 revolve about line y =4 revolve about line x =2 5 revolve about line y = -1 6 revolve about line x =-1