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 = 5.
asked by
James

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)posted by Steve
Respond to this Question
Similar Questions

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 
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 
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, 
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? so then you integrate it 
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 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, 
Calculus
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y= 2e^(−x), y= 2, x= 6; about y = 4. How exactly do you set up the integral? I know that I am supposed to 
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 
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