Formulas:

Shell Method: dV = 2pi(radius) * (height) * (thickness)

Disk method: dV = pi(radius)^2 * (thickness)

Question 1 (26-3-15)

Statement

Using Shell method, find the volume generated by revolving the region bounded by the given curve about the x-axis.

x = 4y - y^2 - 3, x = 0

Attempt

integrating:

4y^2 - y^3 - 3y = x

4/3y^3 - 1/4y^4 - 3/2y^2

at this point I would plug a boundary number into the variable, what number should it be?

Question 2 (26-3-19)

Statement

Using disk method, find the volume generated by revolving the region bounded by the given curve about the y axis.

y = 2(x^1/2), x = 0, y = 3

Attempty/2 = x^1/2

(y/2)^2 = x

y^2/4

(y^2/4)^2

y^4/16

is this the correct path?

Question 3 (26-3-21)

StatementUsing shell method, find the volume generated by revolving the region bounded by the given curve about the y axis.

x^2 - 4y^2 = 4, x = 3

Attempt

2pixy principal formula

isolate y

-4y^2 = 4 - x^2

-y^2 = (4-x^2)/4

-y^2 = -x^2

x = y

2pix^2 = 1/3x^3 = 9

but this answer is incorrect

Thank you for your time.