volume integral app problem

[synx]

using shells method:

y = x^(1/2)

bounded by x=4, y=0

revolved around y-axis

V=2pi * integral(x*x^(1/2)dx) from 0 to 4

Is this right?

 

[galactus]

Which axis are you revolving it about?.

 

[synx]

oh sorry, y-axis

 

[galactus]

Looks OK. \(\displaystyle \L\\2{\pi}\int_{0}^{4}x^{\frac{3}{2}}dx=\frac{128{\pi}}{5}\)

Try it with washers, see if you get the same thing.

\(\displaystyle \L\\{\pi}\int_{0}^{2}(16-y^{4})dy\)