The region R in the first quadrant bounded by the curve y = x2 + 1 and the line y = 3x + 1 is revolved about the line y = 1. SKETCH the solid of revolution and find its VOLUME by i) The Washer Method ii) The Shell Method
9. The region bounded by y = x2, y = 3x, is revolved about the x-axis. a) Sketch the region b) Sketch the solid and a representative disk/washer. c) Set-up the integral to find the volume using disks/washers. DO NOT SOLVE!!!
Use the shell method to find the volume of the solid generated by revolving the region bounded by the line y 3x+10 and the parabola y x2 about the following lines. a. The line x 5 b. The line xE - 2 C. The x-axis d. The line y 25 Use the shell method to find the volume of the solid generated by revolving the region bounded by the line y 3x+10 and the parabola y x2 about the following...
The region Bounded by the curves y=x2 is revolved about the x-axis. Give an integral for the volume of the solid that is generated. The region bounded by the curves y = 3x and y = x' is revolved about the x-axis. Give an integral for the volume of the solid that is generated. va | ndx (Type an exact answer using a as needed.)
show works please Q9 10 Points Let R be the region bounded by the curve y = x2 + 1 and the lines x = 0, x = 1, and y = 1. (a) Set up, but do not evaluate, the volume of the solid obtained by rotating R about the x-axis. Show your work. (b) Set up, but do not evaluate, the volume of the solid obtained by rotating R about the line 2 1. Show your work. =
Find the volume of the solid generated by revolving the region bounded by the curve y 7 sec x and the line y 72 over the interval -+Sxs- about the x-axis. 4 interval--< x 4 about the x-axis The volume is cubic unit(s). (Type an exact answer, using radicals and t as needed.) Find the volume of the solid generated by revolving the region bounded by the curve y 7 sec x and the line y 72 over the interval...
As shown in Fig 1, the line with equation y= 2 - x cuts the curve with equation y = -x2+x+6 at points A and B. y = 2-x y = -x + x + 6 4 (0,0 B Fig 1 (i) Find the coordinates of point A (ii) Calculate the shaded area bounded by the curve, the line and the x-axis as shown in Fig 1
1. Find the volume of the solid obtained by rotating the region bounded by the following curves about the horizontal line y=-3: y=6-x2,y-2, x = 1. 1. Find the volume of the solid obtained by rotating the region bounded by the following curves about the horizontal line y=-3: y=6-x2,y-2, x = 1.
Find the volume of the resulting solid if the region under the curve y = 7/(x2 + 3x + 2) from x = 0 to x = 1 is rotated about the x-axis and the y-axis. (a) the x-axis (b) the y-axis
Find the volume of the solid generated by revolving the region R bounded by the graphs of the given equations about the y-axis. 17)x= x=0, between y=- 4 and y = 4 17) 18) bounded by the circle x2 + y2 = 16, by the line x = 4, and by the line y = 4 18) Find the volume of the solid generated by revolving the region about the given line. 19) The region in the first quadrant bounded...