Intersection for integration

1. Sep 14, 2013

Jbreezy

1. The problem statement, all variables and given/known data

Hi I'm trying to find where these two graphs intersect I would like it to be exact but it isn't quite working.
If I have y = tan(x) and y = x^1/3 how can I solve exactly?
2. Relevant equations

tan(x) = x^1/3 ??? Hmm.
I'm not sure. I don't want arctan popping up on the right side. So I don't know really.

3. The attempt at a solution

2. Sep 14, 2013

Ray Vickson

3. Sep 14, 2013

Jbreezy

I'm supposed to just set up the integral not evaluate it. They want me to consider y = tanx and y = x^1/3 in the first quadrant.
V = 2PI (integral) x(tanx-x^1/3) dx
Between what ever result I get for the intersection of 0 and tanx = x^1/3
and for about y I have
V = 2PI( integral) y(arctan(y) - y^3) dy
Between 0 and whatever y^3 = arctan(y) intersections is.

4. Sep 14, 2013

Jbreezy

This is my work
tan(x) = x^1/3
x = arctan(x^1/3) ok ..... now i'm stuck

5. Sep 14, 2013

Ray Vickson

That's because there is (very probably) no closed-form solution; just use a numerical method.

6. Sep 15, 2013

Jbreezy

What do you mean a numerical method and how am I supposed to indicate the upper bound my teacher gives 0's for decimals. Also does my integrals look OK?

7. Sep 15, 2013

Jbreezy

Do my integrals look set up properly? Also how am I supposed to write an upper limit? Like integral from 0 to
tan(x) = x^1/3? Because I can't really solve this but I have to represent it exactly.