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Disks
Washers
Shells
100
Y=4-x^2 and y=0 on [-2, 2] about x axis
What is v= pi integral from -2 to 2 (4 - x^ 2) -^ 2 dx
100
Y = root x, y= x^2 revolved around x- axis
What is v= pi integral from 0 to 1 (root x) ^ 2 - (x^2)^2 dx
100
Y = 1/x , x= 1, x= 3, y= 0 about the y- axis
What is 2pi integral from 1 to 3 (x times 1/x) dx
200
X= y^2, y= 2, x= 0 about y-axis
What is v= pi integral from 0 to 2 (y^2) ^ 2 dy
200
Y = root x, y = x^2 about x= 1
What is v= pi integral from 0 to 1 [ (1- y^2) ^2 - (1 - root y)^2 ] dy
300
Y=1, y= 2-x^2 about line y=1
What is v= pi integral from -1 to 1 [(2-x^2) - 1) ]^2 dx
300
Y = 2, y= 4-x^2 about x-axis
What is pi integral from -root 2 to root 2 [ (4-x^2) ^ 2 - 2^2 ] dx
400
X= 1, y= x ^3, y= 0 about line x= 1
What is v= pi integral from 0 to 1 (1 - cubed root of y) ^2 dy
400
Y= root x, y= x revolved around y axis
What is v= pi integral from 0 to 1 [ y^2 - y^4] dy
500
Y= root 9-x, y = 0, x= 0 about y axis
What is pi integral from 0 to 3 (9-y^2) ^2 dy
500
Y = x^ 3, y= x^ 2 about x = 1
What is pi integral from 0 to 1 (1-root y ) ^ 2 - (1- cubed root y) ^ 2