Volume Shell Method: Setup & Evaluation

[chapsticks]

Homework Statement

Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the y-axis.
y = √x

Homework Equations

V=2∏∫p(x)h(x) dx
a=0
b=8

The Attempt at a Solution

V=2∏∫(x)(√x)dx
a=0 b=8
=2∏∫(x)^3/2dx
=[(4∏/5)x^5/2]⁸
V= when I do this my answer is wrong and too big

 

[Mark44]

Homework Statement

Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the y-axis.
y = √x

Homework Equations

V=2∏∫p(x)h(x) dx
a=0
b=8

The Attempt at a Solution

V=2∏∫(x)(√x)dx
a=0 b=8
=2∏∫(x)^3/2dx
=[(4∏/5)x^5/2]⁸
V= when I do this my answer is wrong and too big

It looks to me like the interval over which you should be integrating is [0, 9], not [0, 8]. Except for that, I don't seen anything wrong. I get an answer of 972\pi/5 for the volume.

 

[chapsticks]

Wow I should have paid close attention the graph is too small haha thank you.