Question 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

Finding y intecept

0 = 4y - y^2 - 3

Y intercept: 1

Shell method: 2pixy

= 2pi(4y-y^2-3)y

= 2pi(4y^2-y^3-3y)

When I calculate this now with y = 1 the answer is zero, which is wrong.

Question 26-3-21

Statement

Using 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 = 1 - (x^2/4)

y = 1 - x/2

Now to integrate

= 2pix(1 - x/2)

= 2pix - (x^2/2)

not sure how to proceed.

Thanks for looking