Consider the area bound by the line y- xì and y x? where 0 SxS1. Find the volume line of rotation when this area is rotated about a) the x-axis, b) the y-axis, c) the line Consider the area...
1. Use the method of cylindrical shells to find the volume of the following solids rotation (i) Spin the region bound by y -Vx,y 0, x-1 around the y-axis; (ii) Twist the area bound by x -1+(y-2)2 andx- 2 about the x-axis; (iii) Rotate the region between y - x2 and y -6x-2x2 around the y-axis; (iv) Twirl the space between y V and x 2y about the line x 5 2. Use both methods discussed in class to compute...
The given curve is rotated about the y-axis. Find the area of the resulting surface y = 5 - x2 , 0 ≤ x ≤ 4
The region bounded by x = 25 + y x = 0, y = 5, and y = 10 is rotated about the x-axis. Find the volume of the solid of revolution Use your calculator or computer to find the answer rounded to 4 decimal places. Preview The region bounded by x = 25 + y x = 0, y = 5, and y = 10 is rotated about the x-axis. Find the volume of the solid of revolution Use...
The region bounded by f(x)=−2sin(x) x=π, x=2π, and y=0 is rotated about the y-axis. Find the volume of the solid of revolution.
Find the area of the surface generated when the given curve is revolved about the x-axis. 1 y = x² + for SXS1 9 12x The area of the surface is square units. (Type an exact answer, using it as needed.)
Use the following information to answer the questions y=x^2, x=0, y=0 and x=2 Find the area of the region, find the volume of the solid when rotated around the x axis, and find the volume of the solid when rotated around the y axis.
8. Consider the region bounded by the y = x2 - 2x + 1 and y = 1 + 2x - x? Find the area of the region. a. b. Find the volume of the solid when the region is rotated about the x-axis. c. Find the volume of the solid when the region is rotated about the y-axis. d. Find the volume of the solid when the region is rotated about the line x = 5. e. If the...
Find the area of the surface generated when the given curve is revolved about the x-axis. x3 1 1 y = + 12 for 2 sxs1 х The area of the surface is square units. (Type an exact answer, using it as needed.)
1. a A frame B is rotated 60° about the y-axis, 45° about the n-axis, then translated 4 and 6 units relative to the x- and z-axes respectively, then rotated another 30° about the a-axis. Find the new location (10 marks) and orientation of the frame. 0 0 -1 3 -1 0 0 4 1. a A frame B is rotated 60° about the y-axis, 45° about the n-axis, then translated 4 and 6 units relative to the x- and...
4. Find the volume of the solid formed by the curves x = 1-y^4 and x= 0, and rotated about the y-axis 5. Calculate the volume of the solid obtained by rotating the region bounded by the curves y = x^2, y=0, x=-2 https://gyazo.com/cedb31d3c70d20f6947f520b865a0307