Hi. I am not sure if these questions have been posted before. Reworked them today, the answers are not in the book:

Find volume generated by revolving the regions bounded by given curves about y axis

Question 26-3-20

y^2 = x, y = 4, x = 0, Disks

Attempt:

dV = pix^2

x^2=y^4

Integration: pi(1/5)(4^5) = 634.4 ?

Question26-3-22

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

Attempt:

dV = pix^2

(3x^2 - x^3)(3x^2 - x^3) =

6x^4 - 6x^5 + x^6

Intercepts: x = 3 when y = 0

Integration:

pi 6(3^4) - 6(3^5) + 3^6 =

pi (486-1458+729) = -763.4 ?

negative answer is not good

Question26-3-24

x^2 + 4y^2 = 4, Disks

Attempt:

Isolating x: x^2 = 4 - 4y^2

x^2 = 4y - 1/3(4(y^3)) ?

Please let me know if this is correct so far.

Thanks for your time.