Originally Posted by

**Blizzardy** Hi guys! Need help with this question please,

The curve C is defined parametrically by x = (1+t)^(2/3), y = lnt^2, t < than or = to -1

Find the exact volume generated when the area of the region enclosed by C, the lines x = 0, x = 1 and the x-axis is rotated through 2pi radians about the y-axis.

This is my working:

Req. vol. = Vol. of cylinder - Vol. of curve rotated about y axis from y = 0 to y = ln4

(y = ln4 is the intersection b/w C and the line x = 1)

Vol. of cylinder = pi(r^2)(h) = pi(1^2)(ln4) = (pi)(ln4)

For vol. of the curve,

y = ln(t^2) => t = e^(y/2)

Subst. into x = (1+t)^(2/3), x = [1+e^(y/2)]^(2/3)

Vol. of curve = pi * (integrate x^2 dy from y = 0 to y = ln4)

where x^2 = [1+e^(y/2)]^(4/3)

However, the vol. of curve found is much bigger than the vol. of cylinder. What went wrong?