Back9-34. Shell method Let R be the region bounded by the following curves. Use the shell method to find the volume of the solid generated when R is revolved about indicated axis.
y = 1−x²,x = 0, and y = 0, in the first quadrant; about the y-axis
9-34. Shell method Let R be the region bounded by the following curves. Use the shell method to find the volume of the solid generated when R is revolved about indicated axis.
y = √x,y=0, and x=4; about the x-axis
Consider the region R in the first quadrant bounded by y=x^1/n and y=x^n, where n>1 is a positive number.
a. Find the volume V(n) of the solid generated when R is revolved about the x-axis. Express your answer in terms of n.
Use the region R that is bounded by the graphs of y=1+√x,x=4, and y=1 complete the exercises.
Region R is revolved about the x-axis to form a solid of revolution whose cross sections are washers.
b. What is the inner radius of a cross section of the solid at a point x in [0, 4]?
Use the region R that is bounded by the graphs of y=1+√x,x=4, and y=1 complete the exercises.
Region R is revolved about the x-axis to form a solid of revolution whose cross sections are washers.
d. Write an integral for the volume of the solid.
Use the region R that is bounded by the graphs of y=1+√x,x=4, and y=1 complete the exercises.
Region R is revolved about the y-axis to form a solid of revolution whose cross sections are washers.
b. What is the inner radius of a cross section of the solid at a point y in [1, 3]?
Use the region R that is bounded by the graphs of y=1+√x,x=4, and y=1 complete the exercises.
Region R is revolved about the y-axis to form a solid of revolution whose cross sections are washers.
c. What is the area A(y) of a cross section of the solid at a point y in [1, 3]?
Use the region R that is bounded by the graphs of y=1+√x,x=4, and y=1 complete the exercises.
Region R is revolved about the y-axis to form a solid of revolution whose cross sections are washers.
d. Write an integral for the volume of the solid.
Region R is revolved about the line y=1 to form a solid of revolution.
a. What is the radius of a cross section of the solid at a point x in [0, 4]?
Region R is revolved about the line y=1 to form a solid of revolution.
c. Write an integral for the volume of the solid.
Region R is revolved about the line x=4 to form a solid of revolution.
a. What is the radius of a cross section of the solid at a point y in [1, 3]?
For the following regions R, determine which is greater—the volume of the solid generated when R is revolved about the x-axis or about the y-axis.
R is bounded by y=4−2x, the x-axis, and the y-axis.
For the following regions R, determine which is greater—the volume of the solid generated when R is revolved about the x-axis or about the y-axis.
R is bounded by y=1−x^3, the x-axis, and the y-axis.
For the following regions R, determine which is greater—the volume of the solid generated when R is revolved about the x-axis or about the y-axis.
R is bounded by y=x^2 and y=√8x.
Let R be the region bounded by the following curves. Find the volume of the solid generated when R is revolved about the given line.
x=2−secy,x=2,y=π/3, and y=0; about x=2