Volume Integration Problems Need Help (1 Viewer)

[Nasonex]

1. Find the volume of the solid fomed when the curve y= square root of 4-x squared is rotated about the y-axis from y = 1 and y = 2.

2. Find the volume of the solid fomed when the line x + 3y - 1 = 0 is rotated about the y-axis from y = 1 and y = 2.

3. Find the volume of the solid fomed when the line x + 3y - 1 = 0 is rotated about the x-axis from y = 1 and y = 2.

4. The curve y = x cubed is rotated about the y-axis from y = 0 to y = 1. Find the volume of the solid formed.

 

[tommykins]

1. Find the volume of the solid fomed when the curve y= square root of 4-x squared is rotated about the y-axis from y = 1 and y = 2.

2. Find the volume of the solid fomed when the line x + 3y - 1 = 0 is rotated about the y-axis from y = 1 and y = 2.

3. Find the volume of the solid fomed when the line x + 3y - 1 = 0 is rotated about the x-axis from y = 1 and y = 2.

4. The curve y = x cubed is rotated about the y-axis from y = 0 to y = 1. Find the volume of the solid formed.

1. is a tad confusing, what's 4-x squared? please use some brackets, because the square root of 4-x squared (assuming [4-x]) is 4-x?

2.
x = -3y+1
x² = (-3y+1)² = 9y²-6y+1

V = pi [ int 9y²-6y+1 dy ] 2->1
= pi [ 3y³-3y²+y ] 2->1
= pi [ (24-12+2) - (3-3+1) ]
= pi [ 14 - 1 ]
= 13pi.

3. y = x³
x = cubed root y
x² = (cubed root y)² = (y^1/3)^2
= cubed root of y²

V = pi [int (y^2/3) dy]1->0
= pi [ (3y^5/3)/5 ] 1-> 0
= pi [ (3(1)^5/3)/5 ]
= 3pi

Sorry if theres any mistakes, im tired and its a bitch doing it online.

 

[tacogym27101990]

1. Find the volume of the solid fomed when the curve y= square root of 4-x squared is rotated about the y-axis from y = 1 and y = 2.

its obviously just a semi-circle tommykins.

the volume around y axis is ∏∫(x^2)y

do x^2=4-y^2 (squaring both sides)

.........2
so v=∏∫4-(y^2)dy
........1
..............................2
v=∏[4y-{(y^3)/3}]
..............................1
= 5∏ u^3
.........3

 

[tommykins]

ta, got confused.

 

[tacogym27101990]

no worries mate.
how you finding 4 unit??
how much have u done?