Calculus
posted by Leona on .
Volume problem:
y=x^3, x=y^3; rotated about xaxis
I first made y=x^1/3, then x^3=x^1/3
Then I tried to do an integration from 0 to 1 with x^1/3x^3, but I can't get one of the possible answers, which are:
A. 16/35π
B. 16/7π
C. 18/35
D. 7/2
E. 16π
Any advice?

 = integrate symbol
y = x^3
y^3 = x, y = x^(1/3)
Using the formula
pi  (f(x))^2  (g(x))^2 dx
pi  (x^3)^2  x^(1/3)^2 dx
pi  (x^6)  x^(2/3) dx
pi ( 1/7 x^7  3/5 x^(5/3))
When I evaluated from 0 to 1,
I got,
 16/35 pi 
Correction for above,
 = integrate symbol
y = x^3
y^3 = x, y = x^(1/3)
Using the formula
pi  (f(x))^2  (g(x))^2 dx
pi  x^(1/3)^2  (x^3)^2 dx
pi  x^(2/3)  (x^6) dx
pi ( 3/5 x^(5/3)  1/7 x^7 )
When I evaluated from 0 to 1,
I got,
16/35 pi