I will add a few attempts:

26-3-8Rotate about x-axis, use shell method, determine volume:

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

dV = 2pixy

Isolate x

x = y^2

dV = 2pi(y^2)y

dV = 2piy^3

dV = 1/4y^4

dV = 2pi(1/4(2^4)) = 25.132

Is this correct? Thanks.

26-3-10Rotate about x-axis, use disk method, determine volume:

y = 4x - x^2

y = 0

dV = piy^2

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

y = 16x^2 - 4x^3 - 4x^3 + x^4

y = 16x^2 - 8x^3 + x^4

0 = 4x-x^2

I'm stuck trying to find a limit here.

26-3-12Rotate about x-axis, use shell method, determine volume:

y = x^2, y = x

dV = 2piy^2

y^2 = (x^2)^2

y^2 = x^4

1/4x^4

is this the correct path to take? Thanks.