Calculus
posted by James
Write the integral in one variable to find the volume of the solid obtained by rotating the firstquadrant region bounded by y = 0.5x^2 and y = x about the line x = 5.

Steve
using shells,
v = ∫[0,2] 2πrh dx
where r = 5x and h=x0.5x^2
or, using discs,
v = ∫[0,2] π(R^2r^2) dy
where R=5y and r=5√(2y)
Respond to this Question
Similar Questions

calculus
Sketch the region bounded by the curves y = x^2, y = x^4. 1) Find the area of the region enclosed by the two curves; 2) Find the volume of the solid obtained by rotating the above region about the xaxis; 3) Find the volume of the … 
Calculus
a) Find the volume formed by rotating the region enclosed by x = 6y and y^3 = x with y greater than, equal to 0 about the yaxis. b) Find the volume of the solid obtained by rotating the region bounded by y = 4x^2, x = 1, and y = 0 … 
CALCULUS MAJOR HELP!!!!!!
Find the volume of the solid obtained by rotating the region bounded y = 16 x and y = 2 x^2 about y =0 Find the volume of the solid obtained by rotating the region bounded about the xaxis by y=4x^2, x =1, and y = 0 Find the volume … 
Calculus volume stuff
Find the volume of the solid obtained by rotating the region bounded y = 16 x and y = 2 x^2 about y =0 Find the volume of the solid obtained by rotating the region bounded about the xaxis by y=4x^2, x =1, and y = 0 Find the volume … 
Calculus I don't understand
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y = 10 x and y = 5 x^2 about y =0 Find the volume of the solid obtained by rotating the region bounded by y=8 x^2, x … 
Calculus
Consider the solid obtained by rotating the region bounded by the following curves about the line x=1. y=x,y=0,x=4,x=6 Find the volume So it would be pi (integral from 3 to 6) of ((1y)^2 (10)^2) right? 
calculus review please help!
1) Find the area of the region bounded by the curves y=arcsin (x/4), y = 0, and x = 4 obtained by integrating with respect to y. Your work must include the definite integral and the antiderivative. 2)Set up, but do not evaluate, the … 
calculus review please help!
Write the integral in one variable to find the volume of the solid obtained by rotating the first‐quadrant region bounded by y = 0.5x2 and y = x about the line x = 5. Use the midpoint rule with n = 4 to approximate the area of the … 
Please help Calculus
Write the integral in one variable to find the volume of the solid obtained by rotating the first‐quadrant region bounded by y = 0.5x2 and y = x about the line x = 5. 
Calculus
Write the integral in one variable to find the volume of the solid obtained by rotating the firstquadrant region bounded by y = 0.5x^2 and y = x about the line x = 7. I have to use the volume by disks method, but I'm confused about …