Help with Volume of Revolution/Trig Substitution Problem

[student93]

Homework Statement

The problem is attached in this post.

Homework Equations

The problem is attached in this post.

The Attempt at a Solution

Disk method with the radius equal to x/((x^2+3)^5/4)

For Trig Substitution √(x^2+a^2) -> x=atanθ
a=√3 -> a^2=3
x=√(3)tanθ -> dx=√(3)sec^2(θ)
x^2=3tan^2(θ)Volume=π∫((3tan^2(θ)√(3)sec^2(θ))/(3tan^2(θ)+3)^5/4 from 0 to π/6

I can't seem to simplify the integral to the point where I can get the answer etc.

The answer is π/72

 

[tiny-tim]

hi student93!

(try using the X² button just above the Reply box )

i haven't checked, it's too difficult to read , but you seem to have inserted an extra tanθ somewhere …

π∫((3tan(θ)√(3)sec²(θ))/(3tan²(θ)+3)^5/4 can be simplified