Find the volume between y=lnx and x=0 on the interval y=1 and y=2.?

Question

Rotated along the y-axis

Answer 1

x=e^y and
V=Int(1,2) pi*e^2y dy = pi/2 e^2y (1,2) =pi/2(e^4-e^2)

Answer 2

The formula is : integer between - a million and a million of : pi * y² dx y² = (a million - x²)² = a million - 2x² + x^4 the primitive function is : x - 2/3 x^3 + a million/5 x^5 then the quantity is : pi [(a million - 2/3 + a million/5) - (-a million + 2/3 - a million/5)] = pi * [2 - 4/3 + 2/5] = (sixteen pi)/15 No ?