Arc legth of curve C in first octant

[moneyjane]

Let C be the curve obtained by intersecting the sphere x^2 + y^2 + z^2 = a^2 with the surface root(x^2 + y^2)cosh(arctan(y/x))=a.
Find the length in the first octant that joins the points A (a,0,0) and B(x,y,z).


Im not sure what to do. Should i change it into different types of coordinates?

 

[tiny-tim]

Welcome to PF!

Hi moneyjane! Welcome to PF!

(have a square-root: √ and a theta: θ and try using the X² tag just above the Reply box )

Im not sure what to do. Should i change it into different types of coordinates?

Yup … looks like it would be a lot simpler if you changed to cylindrical coordinates (r,z,θ) with r = √(x²+ y²) and tanθ = y/x